JEE Main Physics - Work Energy and Power
Exam Duration: 60 Mins Total Questions : 30
A particle moved from position \(\overrightarrow { { r }_{ 1 } } =3\widehat { i } +2\widehat { j } -6\widehat { k } \) to position \(\overrightarrow { { r }_{ 2 } } =14\widehat { i } +13\widehat { j } +9\widehat { k }\) under the action of a force \((4\widehat { i } +\widehat { j } -3\widehat { k })\) newton .Find the work done .
- (a)
10 J
- (b)
100 J
- (c)
0.01 J
- (d)
1 J
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 of mass 1kg is initially at rest is moved by a horizontal force of 0.5 N on a smooth frictionless table. The value of work done by this force in 10 s is
- (a)
10.9 J
- (b)
13.1 J
- (c)
14.3 J
- (d)
12.5 J
Body of mass M is much heavier than the other body of mass m. The heavier body with speed v collides with the lighter body which was at rest initially elastically.
The speed of lighter body after collision is
- (a)
2 v
- (b)
3 v
- (c)
v
- (d)
v/2
A mass m moves with a velocity v and collides inelastically with another identical mass. After collision, the 1st mass moves with velocity \(v/\sqrt { 3 } \) in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision.
- (a)
v
- (b)
\(\sqrt { 3v } \)
- (c)
\(\frac { 2 }{ \sqrt { 3 } } v\)
- (d)
\(\frac { v }{ \sqrt { 3 } } \)
If a person is pushing a box inside a moving train, the work done in the frame of the earth will be:
- (a)
\(\overrightarrow { F } .{ \overrightarrow { s } }_{ 0 }\)
- (b)
\(\overrightarrow { F } .\overrightarrow { s } \)
- (c)
\(\overrightarrow { F } .(\overrightarrow { s } +\overrightarrow { { s }_{ 0 } } )\)
- (d)
zero
A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively:
- (a)
\(\frac { S }{ 4 } ,\frac { 3gS }{ 2 } \)
- (b)
\(\frac { S }{ 4 } ,\frac { \sqrt { 3gS } }{ 2 } \)
- (c)
\(\frac { S }{ 2 } ,\frac { \sqrt { 3gS } }{ 2 } \)
- (d)
\(\frac { S }{ 4 } ,\sqrt { \frac { 3gS }{ 2 } } \)
A body is acted upon by a force which is proportional to the distance covered. If distance covered be denoted by x, then work done by the force will be proportional to:
- (a)
x
- (b)
x2
- (c)
x3/2
- (d)
none of these
A ball is thrown vertically upwards with a velocity of 10 m/s. It returns to the ground with a velocity of 9 m/s. If g = 9.8 m/sec2, then the maximum height attained by the ball is nearly:
- (a)
5.1 m
- (b)
4.1 m
- (c)
4.61 m
- (d)
5.0 m
An inelastic ball is dropped from a height of 100 m. Due to the earth, 20% of its energy is lost. To what height will the ball rise?
- (a)
80 m
- (b)
40 m
- (c)
60 m
- (d)
20 m
A machine has an efficiency of 25%. Energy is fed into the machine at the rate of 1 kW. The output of the machine is:
- (a)
40 W
- (b)
250 W
- (c)
750 W
- (d)
25 kW
The earth circles the sun once a year. The work which would have to be done on the earth to bring it to rest relative to the sun is: (Ignore the rotation of the earth about its own axis. Given that mass of the earth = 6 \(\times\) 1024 kg and distance between the sun and the earth is 1.5 \(\times\) 108 km)
- (a)
2.7 \(\times\) 1030 J
- (b)
2.7\(\times\) 1031 J
- (c)
-2.7 \(\times\) 1033 J
- (d)
2.7 \(\times\)1033 J
A particle of mass m, is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as, ac = k2 rt2, where k is a constant. The power delivered to the particle by the forces acting on it, is:
- (a)
zero
- (b)
mk2 r2 t2
- (c)
mk2r2t
- (d)
mk2rt
A stone is projected vertically upto reach maximum height h. The ratio of its KE to its potential energy at a height (4/5)h, will be:
- (a)
5 : 4
- (b)
4 : 5
- (c)
1 : 4
- (d)
4 : 1
A parrot is in a cage which is hanging from a spring balance. Initially the parrot sits in the cage and in the second instance the parrot flies about inside the cage.
- (a)
The reading of the balance will be greater when the parrot flies in the cage.
- (b)
The reading of the balance remains unchanged.
- (c)
The reading of the balance will be less when the parrot flies.
- (d)
None of the above
A U238 nucleus initially at rest emits an \(\alpha\)-particle and is converted into Th234. If the KE of \(\alpha\)-particle be 4.1 MeV, the KE of the residual Th234 nucleus is:
- (a)
6.8 MeV
- (b)
0.68 MeV
- (c)
0.07008 MeV
- (d)
0.0068 MeV
At certain point, the potential and kinetic energies of a body of mass 100 gm projected vertically up are 3.6 \(\times\) 107 erg and 6.2 \(\times\) 107 erg respectively. The maximum height reached by the body and the velocity with which it is projected from the ground are:
- (a)
10 m, 14 m/s
- (b)
15 m, 19 m/s
- (c)
10 m, 24 m/s
- (d)
20 m, 17 m/s
A particle of mass 5 m initially at rest explodes into three fragments with mass ratio 3 : 1 : 1. Two of the fragments each of mass m are found to move with a speed 60 m/s in mutually perpendicular directions. The velocity of third fragment is:
- (a)
\(60\sqrt { 2 } \) ms-1
- (b)
\(20\sqrt { 3 } \) ms-1
- (c)
\(10\sqrt { 2 } \) ms-1
- (d)
\(20\sqrt { 2 } \) ms-1
Two billiard balls of the same size and mass are in contact on a billiard table. A third ball of the same size and mass strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the balls is:
- (a)
\(\frac { 1 }{ 2 } \)
- (b)
\(\frac { 3 }{ 2 } \)
- (c)
\(\frac { 2 }{ 3 } \)
- (d)
\(\frac { 3 }{ 4 } \)
A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 111. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m, above the ground. The velocity attained by the ball is:
- (a)
10 m/s
- (b)
30 m/s
- (c)
40 m/s
- (d)
20 m/s
The potential energy of a 1 kg particle free to move along the x-axis is given by:
\(V(x)=\left( \frac { { x }^{ 4 } }{ 4 } -\frac { { x }^{ 2 } }{ 2 } \right) J\)
The total mechanical energy of the particle is 2 J. Then the maximum speed (in m/s) is:
- (a)
2
- (b)
3/\(\sqrt { 2 } \)
- (c)
\(\sqrt { 2 } \)
- (d)
1/\(\sqrt { 2 } \)
Two identical mass M moving with velocity u1 and u2 collide perfectly inelastically. The loss in energy is:
- (a)
\(\frac { M }{ 2 } { ({ u }_{ 2 }-{ u }_{ 1 }) }^{ 2 }\)
- (b)
\(\frac { M }{ 2 } { ({ u }_{ 1 }-{ u }_{ 2 }) }^{ 2 }\)
- (c)
\(\frac { M }{ 4 } { \left( { u }_{ 1 }-{ u }_{ 2 } \right) }^{ 2 }\)
- (d)
\(\\ \frac { M }{ 4 } { \left( { u }_{ 2 }-{ u }_{ 1 } \right) }^{ 2 }\)
In two separate collisions, the coefficients of restitutions 'e1' and 'e2' are in the ratio 3 : 1. In the first collision the relative velocity of approach is twice the relative velocity of separation. Then the ratio between the relative velocity of approach and relative velocity of separation in the second collision is:
- (a)
1 : 6
- (b)
2 : 3
- (c)
3 : 2
- (d)
6 : 1
When a spring is stretched by a distance x, it exerts a force given by:
F =(-5x - 16x3) N.
The work done, when the spring is stretched from 0.1 m to 0.2 m is:
- (a)
8.7 \(\times\) 10-2 J
- (b)
12.2 \(\times\) 10-2 J
- (c)
8.1 \(\times\) 10-1 J
- (d)
12.2 \(\times\) 10-1 J
If the force acting on a body is inversely proportional to its speed, then its kinetic energy is:
- (a)
linearly related to time
- (b)
inversely proportional to time
- (c)
inversely proportional to the square of time
- (d)
a constant