FORCE
1) A rigid body is pivoted at a point. A force of 30 dyne acts on it at a distance of 65cm from the pivot, Calculate the moment of force.
2) A force of 60N produces a moment of force of 12 Nm at a point on a rigid body. Calculate the distance between point of application of force and the turning point.
3) A couple of 12 N force acts on a rigid body such that arm of couple is 60cm. Calculate the moment of couple in SI system.
4) Calculate the resultant moment of the given body.
In which direction will the turning effect be ?
5) A metre scale is balanced at its midpoint by suspending two weights A and B of magnitude 50gf and 25 gf as shown in the figure.
Find the mark on the scale from where the weight B is suspended.
6) A uniform metre scale is balanced on a wedge placed under its 40cm mark at point O. At points A and B, weights of magnitude 60 gf and 20 gf, respectively, are suspended.
The scale is balanced by suspending a weight W at the point C. Calculate the value of W.
7) The handle of a spanner is 25cm long and can tighten a nut if a force of 200 N is applied. if the magnitude of the force applied is 120 N, what is the length of the handle required to tighten the nut ?
8) A uniform metre scale is pivoted at its midpoint. A weight of 20 gf is suspended from one of its end of the scale. Where should a weight of 50 gf be suspended to keep the scale horizontal ?
9) The figure below
shows a balanced see-saw that is 4 m long and pivoted at the centre. A force of 40 N is applied at the end of the see-saw and another force F is applied at a distance of 1.6m from the opposite end on the other side of the privot. Calculate the force F.
10) A uniform metre scale of weight 50 gf is balanced at 60cm mark when a weight of 15 gf is suspended at its 10cm mark. Where must a weight of 100 gf be suspended to balance the matter scale.
Fill in the blanks
1. Centrifugal force is an____ force.
2. Moment of force is also termed as___.
3. Pseudo force is also called as____.
4. The algebraic sum give the ____ sum acting on the body.
5. Force to the right of fulcrum acting downwards produces a ___moment.
6. Weight of a body act at____of the body.
7. ____ movements are considered as positive.
8. Centre of gravity is a___ point.
9. Pair of force is acting on a door is called ____.
10. Torque is the____ effect of force exerted on a beam that is pivoted at a point.
11. Principle of moments is applicable only when the body is in____.
12. In case of___ handles are placed at the extreme to have greater moment of force.
FORCE
1) Moment of force is _____proportional to the distance of the point of application of force and fulcrum.
a) inversely b) directly c) not d) none of these
2) Lesser the force applied____ is the moment of force.
a) greater b) lesser c) equal d) none of these
3) Clockwise moments are considered to be ____
a) positive b) negative c) zero d) all of these
4) _____moments are considered to be positive.
a) clockwise b) anticlockwise c) total d) none of these
5) For equilibrium ___sum of all moments is equal____ some of all anti clockwise moments.
a) arithmetic, arithmetic
b) algebraic, algebraic
c) total, none of
d) all of these
6) The weight of an object lies at the____
a) centre of mass
b) Centre of buoyancy
c) centre of gravity
d) geometric centre always
7) The CG of a regular object would lie____
a) on the body
b) outside the body
c) inside the body
d) all of these
8) the CG of a regular object will depend on ____
a) distribution of mass
b) volume of the body
c) density of the body
d) all of these
9) Longer the size of the key___ it is open a safe vault.
a) easier
b) convenient
c) lesser the force required by
d) none of above
10) Huge trailer trucks have their steering wheel of ____diameter
a) large b) small c) least d) all of these
11) Can a couple pair of forces keep the body in equilibrium ?
a) yes b) no c) data insufficient d) none of these
12) Centre of gravity is____ when it is hollow cone.
a) raised from the base
b) lower towards the base
c) centre the vertical axis
d) none of these
13) C. G of a solid and hollow sphere are____
a) the same b) different c) almost the same d) geometric centre
14) Uniform circular motion has _____.
a) constant speed and variable velocity
b) variable speed and constant velocity
c) circular motion with uniform speed
d) none of these
15) Uniform linear motion has____
a) constant speed, variable velocity
b) constant speed, constant velocity
c) variable speed, constant velocity
d) variable speed, variable velocity
16) When a body moves in a circular path, inward seeking force is called___
a) centrifugal force
b) Tension force
c) Tangential force
d) Centripetal force
17) When a body moves in a circular path, outward force is called a___
a) Pseudo force
b) Centrifugal force
c) cpCentripetal force
d) Reaction force
18) For a body to perform uniform circular motion,____
a) centrifugal force is equal to the centripetal force
b) centrifugal force is less than the cenripetal force
c) Centripetal force is less than centrifugal force
d) centripetal and centrifugal force canal each other
19) Find the maximum force required to open a nut by a spanner of length 50cm producing a torque of 50Nm ?
a) 10N b) 100N c) 0.1 N d) none of these
20) 100 dyne cm is equals to ____Nm.
a) 10⁵ b) 10⁻⁵ c) 0 d) 0.001
21) 10⁻¹⁰ Nm is equal to___ dyne cm.
a) 10⁻⁴ b) 10 c) 0.001 d) none of these
22) Find the weight of half metre scale balance at 5 cm mark when a weight of 10 gf is suspended at one of its ends.
a) 2.5gf b) 100 gf c) 0.2 gf d) 50 gf
23) Find the resultant movement of couple if two equal forces each of 6N are acting at a distance of 3cm each from the centre.
a) 36Nm b) 360 Nm c) 3.6 Nm d) 0.36 Nm
24) Centripetal force is ____while Centrifugal force is____
a) real ,real
b) real, virtual
c) virtual, real
d) virtual, virtual
MORE NUMERICAL PROBLEM
1) A force of 5N is applied at a perpendicular distance of 0.2m from a pivoted point. Calculate the moment of force.
2) The moment of force of 8N about a fixed point is 4Nm. Calculate the distance of the point from the line of action of force.
3) A nut can be opened by a wrench of lengths 50cm with a force of 120N. If a smaller force of 75N is applied, what will be the required length of the handle of the wrench?
4) In the figure, a bicycle wheel of circumference 8m is shown. A force of 4N is applied at the point P in the direction shown. Calculate the moment of force at
a) point O.
b) point Q.
5) Two forces of equal magnitude are acting on a uniform bar AB of length 6m, which is pivoted in the centre of shown in the figure. Determine the magnitude of moment of force. 
a) at the end A.
b) at the end of B.
c) total amount moment of couple.
6) Two forces F₁=5N and F₂ = 8N are acting at points P and Q of a rod pivoted at a point O such that OP= 8m and OQ= 2m.
Calculate the
a) moment of force F₁ at point O,
b) moment of force F₂ at point O.
c) total moment of the two forces at point O.
7) A uniform meter scale is balanced at 60cm mark, when weights of 5gf and 40gf are suspended from 10cm mark and 80cm mark, respectively. Calculate the weight of the meter scale.
8) A uniform metre scale weighing 100gf is pivot at a point O, a 25cm mark. A 80gf weight is hung from 10cm mark and a 30gf weight is hung from 70cm mark as shown in the figure.
Calculate
a) the total anticlockwise moment about point O.
b) The total clockwise moment about point O.
c) the net resultant moment.
9) A uniform metre scale of mass 50g is balanced on the edge of a knife at mark 60cm by suspending an unknown mass at the 80cm mark. Find the value of the unknown mass.
10) A see-saw of 8m long is balanced in the middle. Two children of mass 30kgf and 40 kgf are sitting on the same side of the fulcrum at a distance of 1.5m and 3.5m respectively, from the fulcrum. At what distance must an adult person of weight 60 kgf sit from the fulcrum so as to balance the see-saw?
11) A uniform metre scale of weight 20gf is pivoted at its zero mark. Calculate
a) the moment of force that depress the scale .
b) what would be the magnitude of least force applied on it to make it horizontal?
12) A uniform metre scale can be balanced at the 70cm mark when a mass of 0.05kg is hung from the 94cm mark
a) Draw the diagram of the arrangement
b) Find the mass of the metre scale.
13) A red bull tin is to be opened by means of a screwdriver as shown in the figure. Find the minimum effort required to flick open the lid ? 
WORK, POWER AND ENERGY
1) A Work of 600 J is done when a force of 30 N is applied on the pedals of a bicycle. What is the distance through which the bicycle moves ? 20m
2) An elevator rises up to a height of 30m carrying passengers with a total mass of 600 kg. Calculate the work done by the elevator. -176400 J
3) A lawn mower is pulled with a force of 500 N directed at an angle of 60° with the ground. Calculate the work done by the mower when it is pulled to a distance of 50m. 12500 J
4) A force of 10N acting on a body at an angle of 60° with the horizontal direction displaces the body through a distance of 2 m along the surface of a floor. Calculate the work done. Now, let another force acting on the body making an angle of 30° with the horizontal do the same amount of work. What is the value of this force to displace the body through the same distance along the surface of the floor ? ( take cos60°= 1/2, cos30°= √3/2). 5, 5.77 N
5) A man with a mass of 70kg runs up a flight of 40 stairs, each 15cm high in 30s. Find the power of the man. (g= 10 m/s²). 140 W
6) A rickshaw puller pulls the rickshaw by applying a force of 100 N. if the rickshaw moves with a constant velocity of 36 kmph, find the power of the rickshaw puller. 1000 W
7) The heart does a work 1.2 J in each heartbeat. How many times per minute does it beat if its power is 1.5 W ? 75
8) A horse exerts a force of 200 N to pull the cart. If the horse cart system moves with a velocity of 36 kmph on the level road, then find the power of horse in terms of horsepower (1 H. P= 750 W). 2.67 H. P
9) Calculate the horsepower of an engine that lifts 10 litres of water from a depth of 50m in 30 min. (Taking g= 10 m/s², density of water= 1000 kg/m³, 1 H. P= 750 W). 3693.33 H. P
10) An electric bulb of 100 W is used for 3 hours per day . Calculate the amount of energy consumed in 5 days. 5.4 x 10⁶ J
VARIOUS FORMS OF ENERGY AND CONSERVATION OF ENERGY
1) Determine the kinetic energy of a roller coaster car with a mass 500 kg and moving with a velocity of 15 m/s. 5.625 x 10⁴ J
2) Energy of 6000 J spent in raising a suitcase of mass 50kg to a vertical height. Calculate the vertical height (take g= 10 m/s²). 12m
3) a body of mass 10 kg is taken from a height of 10m to 20 m. Calculate the increase in its potential energy. (Take g= 10 m/s²). 1000 J
4) A body of mass 2 kg falls from a height of 10m. Calculate the energy possessed by it at any instant of time. (Take g= 10 m/s²). 200 J
5) A body of mass 5 kg is initially at rest. A force of 20 N is applied on it. Calculate the kinetic energy of the body after 10s. 4000 J
6) A rock is dropped from a height of 40m. Determine the velocity with which it strikes the ground. (Take g= 10 m/s²). 28.28 m/s
7) Calculate the work required to be done to slow down a bus with a mass of 2000 kg moving at a velocity of 60 kmph to 36 kmph. 1.78 x 10⁵ J
8) A train weighing 5000 N has a kinetic energy of 10 kJ. Find the velocity of the train. (Take g= 10 m/s²). 6.32 m/s
9) How will the kinetic energy of a car change if
a) its mass is trippled. Tripled
b) its velocity is doubled. Four times
c) its mass is doubled and velocity is halved? Halved
10) What will be the ratio r kinetic energy of two buses with equal mass moving with different velocities if velocity of bus A is 10 m/s and velocity of bus B is 12.25 m/s ? 2:3
11) A body mass 0.5 kg has a momentum of 30 kg m/s. Calculate the kinetic energy of the body. 900 J
12) An object of mass 10 kg is raised to a height of 20m above the ground level. What is its potential energy ? if the object is allowed to fall, find its kinetic energy when it is at a height of 5m above the ground. (Take g= 10 m/s). 200 J, 1500 J
13) A bullet of mass 3g travels with a speed of 600 M/s. It penetrates a wall that offers resistive force of 600 N to the motion of the bullet find
a) the initial kinetic energy of the bullet. 540 J
b) the distance through which the bullet has penetrating before coming to rest. 0.9m
c) the speed with which the bullet emergence out of the wall if its thickness is 0.7m. 282.8 m/s
14) A body of mass 2kg is thrown vertically upwards with an initial velocity of 50 m/s. Calculate
a) the initial kinetic energy impartu to the body. 2500 J
b) the maximum height if friction due to air is neglected. 125m
c) the maximum height reached if 25% of the initial energy is lost against air friction. 93.75 m
15) An oscillating simple pendulum rises to a maximum vertical height of 6 m at its extreme positions . if the mass of the bulb 300g, find
a) the velocity of the bob at its resting position. 1.09 m/s
b) the total energy of the pendulum at any instant while oscillation (take g= 10 m/s²). Neglect the friction due to air. 0.18 J
WORK, POWER AND ENERGY
1) Work done= force x _____
a) distance b) time c) velocity d) displacement
2) SI unit of work is ____
a) newton b) Joule c) erg d) dyne
3) 1 dyne cm =_____
a) 1 erg b) 1 newton cm c) 10 newton cm d) none of these
4) Work done is a____ quantity.
a) pure b) scalar c) vector d) dimensionless
5) Work done is positive when _____
a) distance is positive
b) maximum distance travelled along direction of force applied.
c) displacement is in direction of force applied
d) distance is negative
6) Work done by buoyant force is ____
a) positive b) negative c) zero d) cannot definitely say
7) A parrot flying at a height of 300m above sea level applying a force of 10N___
a) does not work
b) does work equal to 3000 J
c) does negative work
d) none of these
8) A sprinter running in a 200m x 4 medley relay circular track does not do any work. Is this statement always true ?
a) yes b) no c) incomplete data d) none of these
9) 8J= ____ kWh.
a) 3.6 x 10⁶
b) 0.278 x 10⁻⁶
c) 3.6 x 10⁻⁶
d) none of these
10) Power = ___
a) work x time
b) time x work
c) time/work
d) work/time
11) SI unit of power is _____
a) watt hour
b) kilowatt
c) watt
d) joule hour
12) 1000 watt = ____
a) 10⁶ b) 10⁹ c) 10⁻¹² d) 10⁻³
13) 1 kW= ____
a) 1000W
b) 100J/100 sec
c) 1000 J/1000 sec
d) 10⁻³ W
14) Force= Power x ____
a) velocity b) (velocity)² c) 1/Velocity d) √velocity
15) Gravitational potential energy= ___
a) mgh b) mv²/2 c) 2mgh d) none of these
16) kinetic energy of body is independent of ___
a) force applied
b) time for which force is applied
c) elasticity of the body
d) none of these
17) When a body travels in a circular path and covers a distance equals to 1/4th of its circumference can we conclude that work done is zero?
a) yes b) no c) both a and b d) none of these
18) When a body travels a circular path such that its displacement is maximum equal to the diameter of the circle can we conclude work done is zero.
a) yes b) no c) data insufficient d) none of these
19) Power rating of a pump=
a) power work output x power input
b) power input/ power output
c) power output/time
d) power output/power input
20) Power rating of a rotary pump is____
a) mv²/2 b) work input x time
c) work input x time
d) work output/work input
21) Energy is____
a) the capacity to use Power
b) capacity to produce power
c) capacit to do work
d) capacity to do work per unit time
22) The two basic forms of mechanical energy are:
a) PE and KE
b) sound and light
c) heat and tidle
d) solar and wind
23) In an oscillating pendulum, KE is____ at extremes.
a) zero
b) negative
c) positive
d) none of these
24) In an oscillating pendulum the ____energy is maximum at extremes .
a) potential
b) vibration
c) Gravitational potential
d) Kinetic
25) For a freely falling body the potential energy at the top____.
a) is zero
b) is completely converted to KE
c) is equals to gravitational potential energy
d) is minimum
26) During freefall the total energy are 3/4th the height is ____
a) constant b) zero
c) gravitational potential energy at the top
d) 3/4th the initial potential energy
27) In a washing machine the electrical energy is converted into____
a) sound energy
b) vibration energy
c) kinetic energy
d) mechanical Kinetic rotational energy
28) In the case of a catapult____energy gets converted into kinetic energy.
a) muscular
b) stretchable
c) elastic potential
d) elastic
29) In a photovoltaic cell _____energy converts to _____energy.
a) heat, chemical
b) light, electrical
c) light, wind
d) thermal, kinetic
30) Charging of a lead accumulator____energy gets converted into chemical energy.
a) sound b) light c) heat d) electrical
31) If 1kWh is ____ MJ then 8 MJ is_____ kWh.
a) 36,72 b) 3.6,2.22 c) 0.36,222 d) none of these
32) 500 litres of water is _____kg.
a) 5kg b) 50kg c) 500 kg d) none of these
33) For a given mass of a body if velocity is doubled the kinetic energy is ____
a) halved b) 4 times c) 1/4th d) none of these
34) For a given mass and velocity the kinetic energy remains constant if____
a) mass is four times and velocity is half.
b) mass is half and velocity is doubled
c) mass and velocity both are squared
d) none of these
35) If a body mass 5 kg is lifted from the ground level to a height of 5m then the ratio of its inertia is
a) 1:1 b) same c) constant d) not defined
36) During energy transformation some form of energy is given out without it being used anywhere, such energy is called_____
a) back up energy
b) stored energy
c) wasteful energy
d) dissipated form of energy
37) When a substance melt____
a) no energy change takes place.
b) energy change takes place but is totally dissipated
c) PE changes into KE d) none the above
38) When camphor sublimes ____
a) chemical energy changes into heat energy
b) PE gets converted into KE
c) it simply converts into a gaseous state without attaining the liquid state
d) entire energy is lost to the surroundings
39) a person drives a Lamborghini and reaches Delhi while another person travels the same on a bullock cart. Is the work done is the same ?
a) yes b) no c) data insufficient d) work done is zero
40) A boy using a lift to reach 26 floors and a girl climbing the stairs to reach the 26th floor does the same work. Comment whether true or false ?
a) yes
b) data in complete
c) no
d) boy spend more energy than girl.
FILL IN BLANKS
1) The capacity do work is work is____.
2) Work done is zero when___ displacement is zero.
3) Energy can neither be created nor destroyed is the____ of energy.
4) Energy by virtue of its state of rest is called___.
5) Energy by virtue of its emotion is called____.
6) SI unit of power is_____.
7) The work done is ____. When angle between force and displacement is 90°.
8) Rate of doing work per unit time is____.
9) Power is forcex ___.
10) Work done is____. When displacement is against the direction of applied force.
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