Physics - Work, Energy and Power
Exam Duration: 45 Mins Total Questions : 30
A bullet of mass A and velocity B is fired into a block of mass C and sticks to it. The final velocity of system equals
- (a)
\({B\over A+B}B\)
- (b)
\({A\over A+C}B\)
- (c)
\({A+B\over C}A\)
- (d)
\({A+C\over B}\)
A shell fired from a cannon explodes in mid-air. Then
- (a)
its total momentum increases
- (b)
its total momentum decreases
- (c)
its total kinetic energy increases
- (d)
its momentum and kinetic energy do not change
Six identical marbles are lined in a straight groove made on a horizontal frictionless surface as shown in the figure. Two similar marbles each moving with velocity \(\overrightarrow { \vartheta } \) colllide with the row of six marbles from the left. What is observed ?
- (a)
Two marbles from the right roll out with a speed \(\overrightarrow { \vartheta } \) each, the remaining marbles do not move
- (b)
One marble from the right rolls out with a speed of \(2 { \vartheta } \), the remaining marbles do not move.
- (c)
All six marbles in the row will roll out with speed \(\vartheta /6\) each, the two incident marbles will come to rest.
- (d)
After collision, the two marbles on the left move with velocity mass \(\overrightarrow { \vartheta } \) in opposite directions.
A body of mass 0.5 kg travels in a straight line with velocity, v = ax3/2, where a = 5 m-1/2/s. What is the work done by the net force during its displacement from x = 0 to x = 2 m ?
- (a)
3.5 J
- (b)
55 J
- (c)
65 J
- (d)
69 J
The bob of a pendulum has its rest point 1 m below the support. The bob is pulled aside until the string makes an angle of 60o with the vertical line. On release with what speed does the bob swing pass its rest point?
- (a)
3.2 m/s
- (b)
4 m/s
- (c)
2 m/s
- (d)
5 m/s
When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx2 , where a and b are constants. The work done in stretching the unstretched rubber - band by L is
- (a)
\({ aL }^{ 2 }+{ b }L^{ 3 }\)
- (b)
\(\frac { 1 }{ 2 } ({ aL }^{ 2 }+{ bL }^{ 3 })\)
- (c)
\(\frac { { aL }^{ 2 } }{ 2 } +\frac { { bL }^{ 3 } }{ 3 } \)
- (d)
\(\frac { 1 }{ 2 } \left( \frac { { aL }^{ 2 } }{ 2 } +\frac { { bL }^{ 3 } }{ 3 } \right) \)
A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of x-axis is applied to the block. The force is given by: \(\overrightarrow { F } =(4-{ x }^{ 2 })\hat { i } N\) where x is in metre and the initial position of the block is x = 0. The maximum kinetic energy of the block between x = 0 and x = 2.0 m is:
- (a)
2.33 J
- (b)
8.67 J
- (c)
5.33 J
- (d)
6.67 J
A shell explodes and many pieces fly off in different directions. Which of the following is conserved?
- (a)
Kinetic energy
- (b)
Momentum
- (c)
Neither momentum nor KE
- (d)
Momentum and KE
At her maximum height, a girl in a swing is 3 m above the ground and at the lowest point she is 2 m above the ground. What is her maximum velocity?
- (a)
\(\sqrt { 29.4 } \) ms-1
- (b)
\(\sqrt { 9.8 } \)ms-1
- (c)
\(\sqrt { 19.6 } \) ms-1
- (d)
9.8 ms-1
A mass m moving horizontally with velocity V0 strikes a pendulum of mass m. If the two masses stick together after the collision, then the maximum height reached by the pendulum is:
- (a)
\({ v }_{ 0 }^{ 2 }/8g\)
- (b)
\({ v }_{ 0 }^{ 2 }/2g\)
- (c)
\(\sqrt { 2{ v }_{ 0 }g } \)
- (d)
\(\sqrt { { v }_{ 0 }g } \)
A bag P (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system:
- (a)
momentum is \(\frac { mvM }{ M+m } \)
- (b)
kinetic energy is \(\frac { 1 }{ 2 } \)mv2
- (c)
mmentum is \(\frac { mv(M+m) }{ M } \)
- (d)
kinetic energy is \(\frac { { m }^{ 2 }{ v }^{ 2 } }{ 2(M+m) } \)
When two bodies collide elastically, then:
- (a)
KE of the system alone is conserved
- (b)
only momentum is conserved
- (c)
both KE and momentum are conserved
- (d)
neither KE nor momentum is conserved
Two balls at the same temperature collide, which is conserved?
- (a)
Temperature
- (b)
Velocity
- (c)
Kinetic energy
- (d)
Momentum
A neutron moving with velocity u collides elastically with an atom of mass number A. If the collision is head on and the initial kinetic energy of neutron is E, then the final kinetic energy of the neutron after collision is:
- (a)
\({ \left( \frac { A+1 }{ A-1 } \right) }^{ 2 }E\)
- (b)
\({ \left( \frac { A-1 }{ A+1 } \right) }^{ 2 }E\)
- (c)
\(\left( \frac { A-1 }{ A+1 } \right) E\)
- (d)
\(\left( \frac { A+1 }{ A-1 } \right) E\)
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\(\sqrt { 2 } \)
A bullet gets embedded in a solid block resting on a frictionless surface. In this process:
- (a)
momentum is conserved
- (b)
kinetic energy is conserved
- (c)
potential energy is conserved
- (d)
both (a) and (b)
A tennis ball is thrown from a height Ii above the ground. If the ball strikes to the ground with elastic collision, what height will the ball achieve after the third collision?
- (a)
he6
- (b)
e2 h
- (c)
e3 h
- (d)
None of these
The slope of the kinetic energy versus position vector gives the rate of change of:
- (a)
work
- (b)
velocity
- (c)
force
- (d)
power
A shell at rest at the origin explodes into three fragments of masses 1 kg, 2 kg and m kg. The 1 kg and 2 kg pieces fly-off with speeds of 5 ms-1 along x-axis and 6 ms-1 along y-axis respectively. If the m kg piece flies-off with a speed of 6.5 ms-1, the total mass of the shell must be:
- (a)
4 kg
- (b)
5 kg
- (c)
3.5 kg
- (d)
4.5 kg
A body of mass m moving with velocity v makes a head-on collision with another body of mass 2 m which is initially at rest. The loss of kinetic energy of the colliding body (mass m) is:
- (a)
\(\frac { 1 }{ 2 } \) of its initial KE
- (b)
\(\frac { 1 }{ 9 } \) of its initial KE
- (c)
\(\frac { 8 }{ 9 } \) of its initial KE
- (d)
\(\frac { 1 }{ 4 } \)of its initial KE
A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is:
- (a)
40 m/s
- (b)
120 m/s
- (c)
100 m/s
- (d)
80 m/s
A cricket ball of mass 0.5 kg strikes a cricket bat normally with a velocity of 20 ms-1 and rebounds with a velocity of 10 ms-1. The impulse of the force exerted by the ball on the bat is:
- (a)
15 N-s
- (b)
25 N-s
- (c)
30 N-s
- (d)
10 N-s
A pendulum bob of mass m is hanging from a fixed point by a light thread of length l. A horizontal speed v0 is imparted to the bob so that it takes up horizontal position. If g is the acceleration due to gravity, then v0 is:
- (a)
mgl
- (b)
\(\sqrt { 2gl } \)
- (c)
\(\sqrt { gl } \)
- (d)
gl
This question has Statement I and Statement Il. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement-I: A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as
\(f\left( \frac { 1 }{ 2 } { mv }^{ 2 } \right) \) then \(f=\left( \frac { m }{ M+m } \right) \)
Statement-I: Maximum energy loss occurs when the particles get stuck together as a result of the collision.
- (a)
Statement-I is true, Statement-Il is false.
- (b)
Statement-I is false, Statement-II is true
- (c)
Statement-I is true, Satament-II is true, Statement-II is a correct explanation of Statement-I.
- (d)
Statement-I is true, Statement-II is true, Statement-II is not a correct explanation of Statement-I