IISER Physics - Work, Energy and Power
Exam Duration: 45 Mins Total Questions : 30
For a body moving with constant speed in a horizontal cirlce,which of the following remains constant?
- (a)
velocity
- (b)
acceleration
- (c)
centripetal force
- (d)
kinetic energy
A force \(\overrightarrow { { F } } =-K(y\widehat { i } +x\widehat { j })\) (where K is a positive constant ) acts on a particle moving in the x-y plane .Starting from the origin ,the particle is taken along the positive x-axis to the point (a,0) and then parallel to the y -axis to the point (a,a) .The total work done by the force \(\overrightarrow { { F } } \) on the particle is
- (a)
-2 Ka2
- (b)
2 Ka2
- (c)
-K a2
- (d)
Ka2
A particle of mass m is moving in a horizontal circle of radius 'r' under centripetal force equal to \(-{K\over r^{2}}\), where K is constant. Total energy of the particles is
- (a)
\(-{K\over r^{}}\)
- (b)
\(-{K\over 2r^{}}\)
- (c)
\({K\over 2r^{}}\)
- (d)
\({K\over r^{}}\)
A cord is used, to lower vertically a block of mass 'M' a distance 'd' at a constant downward acceleration of g/4. Then the work done by the cord on the block is
- (a)
\(Mgd\over4\)
- (b)
\(-Mgd\over4\)
- (c)
\(3Mgd\over4\)
- (d)
\(-3Mgd\over4\)
A body of mass m1 travelling with velocity \(\upsilon\) suffers head on collision with a mass m2 at rest. Calculate the ratio of the kinetic energy., energy transfer is complete when
- (a)
m1 >m2
- (b)
m1 <m2
- (c)
m1 =m2
- (d)
m1 =2m2
A body is moving undirectionally under influence of a source of constant power. Its displacement in time t is proportional to
- (a)
t1/2
- (b)
t
- (c)
t3/2
- (d)
t2
A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by
- (a)
5.5 cm
- (b)
2.5 cm
- (c)
11.0 cm
- (d)
8.5 cm
The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest under the action of a constant force, is directly proportional to:
- (a)
\(\sqrt{m}\)
- (b)
independent of m
- (c)
\({1\over \sqrt{m}}\)
- (d)
m
The centripetal acceleration of a particle varies inversely with the square of the radius r of the circular path. The kinetic energy of the particle is directly proportional to:
- (a)
r
- (b)
r2
- (c)
r-1
- (d)
r-2
A bullet when fired at a target with a velocity of 100 m/sec penetrates one metre into it. If the bullet is fired at a similar target with a thickness 0.5 metre, then it will emerge from it with a velocity of:
- (a)
\(50\sqrt { 2 } \) m/s
- (b)
\(\frac { 50 }{ \sqrt { 2 } } \)m/s
- (c)
50 m/s
- (d)
10 m/s
Two bodies M and N of equal masses are suspended from two separate springs of spring constants K 1 and K 2 respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to that of N is:
- (a)
\(\frac { { K }_{ 1 } }{ { K }_{ 2 } } \)
- (b)
\(\sqrt { \frac { { K }_{ 1 } }{ { K }_{ 2 } } } \)
- (c)
\(\frac { { K }_{ 2 } }{ { K }_{ 1 } } \)
- (d)
\(\sqrt { \frac { { K }_{ 2 } }{ { K }_{ 1 } } } \)
Two bodies with kinetic energies in the ratio of 4:1 are moving with equal linear momentum. The ratio of their masses is:
- (a)
1 : 2
- (b)
1 : 1
- (c)
4 : 1
- (d)
1 : 4
A rectangular block has dimensions 8 m \(\times\) 4 m \(\times\) 2 m. It has a mass of 100 kg. It is initially on the ground with the shortest side vertical. If it is to be turned so that the longest side is vertical, the work done is equal to:
- (a)
29.4 J
- (b)
2.94 \(\times\) 103 J
- (c)
58.8 \(\times\) 102 J
- (d)
580 J
A bullet having a speed of 100 m/sec crashes through a plank of wood. After passing through a plank, its speed is 80 m/sec. Another bullet of the same mass and size, but travelling at 80 m/sec, is fired at the plank. The speed of the second bullet after travelling through the plank is: (Assume that resistance of the plank is independent of the speed of the bullet)
- (a)
\(10\sqrt { 7 } m{ s }^{ -1 }\)
- (b)
\(20\sqrt { 7 } { ms }^{ -1 }\)
- (c)
\(30\sqrt { 7 } { m }s^{ -1 }\)
- (d)
\(20\sqrt { 5 } { ms }^{ -1 }\)
A bullet of mass m is fired with certain velocity from a gun of mass M. Gun, which is attached with one end of spring, compresses it by distance d. If k is spring constant, then velocity of bullet is:
- (a)
d/M\(\sqrt { km } \)
- (b)
d/m \(\sqrt { km } \)
- (c)
md \(\sqrt { 1/km } \)
- (d)
mk\(\sqrt { 1/dM } \)
A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from v1 to v2 is: (neglect friction)
- (a)
\(\frac { 3P }{ m } \left( { v }_{ 2 }^{ 2 }-{ v }_{ 1 }^{ 2 } \right) \)
- (b)
\(\frac { m }{ 3P } ({ v }_{ 2 }-{ v }_{ 1 })\)
- (c)
\(\frac { m }{ 3P } ({ v }_{ 2 }^{ 3 }-{ v }_{ 1 }^{ 3 })\)
- (d)
\(\frac { m }{ 3P } \left( { v }_{ 2 }^{ 2 }-{ v }_{ 1 }^{ 2 } \right) \)
A block is released from the top of a smooth inclined plane of inclination \(\theta\). Let v be the speed of the particle after travelling a distance s down the plane. Then which of the following will remain constant?
- (a)
v2 + 2gs sin \(\theta\)
- (b)
v2 - 2gs sin \(\theta\)
- (c)
v2 - \(\sqrt { 2gs } \)sin \(\theta\)
- (d)
v+\(\sqrt { 2gs } \) sin \(\theta\)
On a stationary sail boat air is blown from a fan attached to the boat. The boat will:
- (a)
not move
- (b)
spin around
- (c)
move in the direction in which air is blown
- (d)
move in a direction opposite to that in which air is blown
In perfectly inelastic collisions, the relative velocity of the bodies:
- (a)
before impact is zero
- (b)
before impact is equal to that after impact
- (c)
after impact is zero
- (d)
is characterised by none of the above
A particle of mass m moving towards the east with speed v collides with another particle of the same mass and same speed v moving towards the north. If the two particles stick to each other, the new particle of mass 2m will have a speed of:
- (a)
v
- (b)
v/2
- (c)
v/\(\sqrt { 2 } \)
- (d)
v\(\sqrt { 2 } \)
An object initially at rest explodes into 3 fragments A, B and C. The momentum of A is p\(\hat { i } \) and that of B is \(\sqrt { 3 } \)p\(\hat { j } \), where p is a +ve number. The momentum of C will be:
- (a)
(l + \(\sqrt { 3 } \))p in a direction making angle 120° with that of A
- (b)
(1 + \(\sqrt { 3 } \))p in a direction making angle 150° with that of B
- (c)
2p in a direction making angle 150° with that of A
- (d)
2p in a direction making angle 150° with that of B
Ball 1 collides with another identical ball at rest. For what value of coefficient of restitution e, the velocity of second ball becomes two times that of 1 after collision?
- (a)
\(\frac { 1 }{ 3 } \)
- (b)
\(\frac { 1 }{ 2 } \)
- (c)
\(\frac { 1 }{ 4 } \)
- (d)
\(\frac { 1 }{ 6 } \)
A ping-pong ball of mass m is floating in air by a jet of water emerging out of a nozzle. If the water strikes the ping-pong ball with a speed v and just after collision water falls dead, the rate of flow of water in the nozzle is equal to:
- (a)
\(\frac { 2mg }{ v } \)
- (b)
\(\frac { mv }{ g } \)
- (c)
\(\frac { mg }{ v } \)
- (d)
none of these
A gun fires bullets each of mass 1 g with velocity of 10 ms-1 by exerting a constant force of 5 g weight. Then the number of bullets fired per second is: (Take g=10 ms-2)
- (a)
50
- (b)
5
- (c)
10
- (d)
25
300 J of work is done in sliding a 2 kg block up an inclined plane of height 10m. Taking g = 10 ms-2, work done against friction is:
- (a)
200 J
- (b)
100 J
- (c)
zero
- (d)
1000 J
A 10 kg object collides with stationary 5 kg object and after collision they stick together and move forward with velocity 4 ms-1. What is the velocity with which the 10 kg object hit the second one?
- (a)
4 ms-1
- (b)
6 ms-1
- (c)
10 ms-1
- (d)
12 ms-1
A bomb of mass 3.0 kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s. The total energy imparted to the two fragments is:
- (a)
1.07 kJ
- (b)
2.14 kJ
- (c)
2.4 kJ
- (d)
4.8 kJ
Three guns are aimed at the centre of a circle. They are mounted on the circle; 120° apart. They fire in a timed sequence, such that the three bullets collide at the centre and mash into a stationary lump. Two of the bullets have identical masses of 4.5 g each and speeds of v1 and v2. The third bullet has a mass of 2.50 g and a speed of 575 m/s. Find the unknown speeds.
- (a)
200 m/s each
- (b)
145 m/s and 256 m/s
- (c)
536 m/s and 320 m/s
- (d)
none of these
A particle of mass m, strikes on ground with angle of incidence 45°. If coefficient of restitution e = \(\sqrt [ 1 ]{ 2 } \), the velocity of reflection is:
- (a)
\(\frac { \sqrt { 3 } }{ 2 } v\)
- (b)
\(\sqrt { 3 } v\)
- (c)
\(\frac { 1 }{ 2 } v\)
- (d)
\(\frac { v }{ \sqrt { 3 } } \)
A bullet of mass 0.05 kg moving with a speed of 80 ms-1 enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the bullet is:
- (a)
300 N
- (b)
20 N
- (c)
400 N
- (d)
40 N
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