6

Q1. If a neutron makes a head-on collision with a stationary deuteron; the fractional energy loss of neutron in the collision is

• 8/27
• 2/3
• 8/9
• 16/81

Solution

In a head-on collision the fractional decrease in energy is given by . Now mass of deuteronis m₂ = 2 x mass of neutron = 2m₁ That is, m₂ = 2m₁ Therefore, fractional decrease in kinetic energy of neutron is

Q2. A moving white hockey puck collides elastically with a stationary red hockey puck on a frictionless horizontal surface. No net external force acts on the two-puck system. Select all of the following statements that must be true for this elastic collision. 1. The kinetic energy of the white puck is conserved (same before and after the collision) 2. The linear momentum of the white puck is conserved. 3. The linear momentum of the two puck system is conserved.

• 1 only
• 3 only
• 1 and 2 only
• 1 and 3 only

Solution

Because in this elastic collision both the kinetic energy and momentum of the system are conserved, the two puck system can have both the kinetic energy and linear momentum exchanged keeping the total constant.

Q3. Which of the following is not a unit of energy?

• kilowatt hour
• electron volt
• joule/metre
• newton metre

Solution

Joule is the unit of energy and joule/metre is the unit of force.

Q4. A hawk of mass 10 kg dives to catch a mouse. During dive it loses 500 J of its potential energy. The height from where it begins its dive is    (take g = 10 m/s²)

• 50 m
• 10 m
• 5 m
• 1 m

Solution

Change in Gravitational Potential Energy = mass x acceleration x change in height 500 J = 10 kg x 10 x change in height Change in height = 5 m So, the hawk dives to catch the mouse at a distance of 5m.

Q5. Select the odd one out

• Viscous force
• Air-resistance
• Electrostatic force
• Frictional force

Solution

Viscous force, air-resistance, frictional forces are path dependent forces, hence these are non-conservative forces. However, electrostatic force is conservative force.

Q6. The work energy theorem holds when work is done by

• only a constant force
• only a variable force
• either constant or variable force
• only a gravitational force

Solution

Work-energy theorem holds for both constant and variable forces.

Q7. A body of mass m moving with a constant velocity v hits another body of the same mass at rest and sticks to it. The velocity of the compound body after the collision is

• v/2
• 2v
• v
• Zero

Solution

By applying the law of conservation of linear momentum, we have mv + 0 = 2mV V = v/2 Then, the velocity of the compound body after the collision will be v/2.  

Q8. A bomb of mass 4 kg explodes in air into two pieces of masses 3 kg and 1 kg. The smaller mass goes at a speed of 90 m/s. The total energy imparted to two fragments is.

• 2.4 kJ
• 5.9 kJ
• 3.8 kJ
• 5.4 kJ

Solution

The bomb was initially at rest and after explosion it separates into two parts which move in opposite directions. Hence, by conservation of momentum, we have 3 x v = 1 x 90 v = 30 m/s Therefore, the total energy imparted to the two fragments is

Q9. Work done in motion of the body over a closed loop for conservative forces is

• zero
• non-zero
• infintesimal
• infinity

Solution

Work done in motion of the body over a closed loop for conservative force is zero.

Q10. Which of the following is the correct relation between kWh and Joule?

• 1 kWh = 3.6 X 10¹² J
• 1 kWh = 3.6 X 10⁶ J
• 1 kWh = 36 X 10⁶ J
• 1 kWh = 1.6 X 10^-19 J

Solution

1 kWh = 3.6 X 10⁶ J

Q11. Frictional force is an example of

• Non conservative force
• Conservative force
• Nuclear force
• Electrostatic force

Solution

Frictional force is a non conservative force.

Q12. Which of the following statement is not related to conservative force?

• Work done in closed path is zero
• Work done is recoverable
• Path dependent
• Path independent

Solution

Path dependent force is a non-conservative force.

Q13. Out of a pair of identical springs of spring constants 240 N/m, one is compressed by 10 cm and other is stretched by 10 cm. The difference in P.E. stored in the two springs is:

• Zero
• 4 J
• 12 J
• 1.2 J

Solution

In both cases the P.E. will be kx²/2. Hence. the difference of energies will be zero.

Q14. You are in a lift moving from the 3^rd floor to the 12^th floor, having a height difference of H = 40 m. Your mass is M = 80 kg and the acceleration due to gravity is g = 10 m/s². If the elevator moves at a constant speed without stopping, what is the total work performed by all of the forces together (the net force) acting on you?

• MgH
• -MgH
• Mg
• 0

Solution

Let us check this from the point of view of forces acting. If the positive y direction is upward, then we have The force due to gravity is -Mg Force applied by the lift is +Mg in the +y-direction The displacement H is upwards The work done is  Work done by gravity on you is W_g = -Mgh and the work done by force from lift is W_a = Mghand hence, the net work done is W = W_g + W_a = -Mgh + Mgh = 0. Since there is no change in speed ΔK = 0 = W.

Q15. Time rate at which work is done by a force is

• Power
• Acceleration
• Torque
• Centrifugal Force

Solution

Time rate at which work is done by a force is Power.

Q16. If momentum of an object is doubled, how does its kinetic energy change?

• increases 4 times
• decreases 4 times
• increases 2 times
• decreases 2 times

Solution

Q17. Which of the following is not correct for the condition for work not to be done:

• force is zero
• displacement is zero, though force is non-zero
• force and displacement are perpendicular to each other.
• force and displacement are at 180 degrees with each other

Solution

When force and displacement are at 180° to each other, then the work done will be negative.

Q18. What is the dimension of k/m where k is the force constant and m is the mass of the oscillating object?

• [T²]
• [T^-2]
• [T^-1]
• [T¹]

Solution

Q19. An engine generates a power of 10 kW.  In how much time will it raise a mass of 200 kg through a height of 40m.

• 4 sec
• 5 sec
• 8 sec
• 10 sec

Solution

Q20. You are in a lift moving from the 3^rd floor to the 12^th floor, through a height H. If the elevator moves at a constant speed without stopping, what is the work performed on you by the elevator? Take your body mass as M.

• MgH
• -MgH
• Mg
• -Mg

Solution

The work performed on you by the elevator is force times displacement = -MgH Negative sign shows it is moving upwards, i.e., against g.

Q21. The potential energy of a hammer of mass 10 kg, lifted to the height of 10 m is

• 100 J
• 10 J
• 98 J
• 980 J

Solution

Potential Energy = mgh = 10 kg x 9.8 ms^-2 x 10 m = 980 J

Q22. Which of the following force is non-conservative?

• Restoring force of spring
• Force between two stationary charges
• Force between two stationary masses
• Human push or pull

Solution

A force is said to be non-conservative, if the work done by it depends upon the path. Human push or pull is non-conservative because it is dependent on the path on which the object is pulled or pushed.

Q23. The potential energy of the spring when stretched

• Does not change
• Increases
• Decreases
• Depends on the material of the spring

Solution

The potential energy of the spring increases because work is done on it when it is stretched.

Q24. When does the potential energy of a spring increase?

• when spring is compressed or stretched
• only when spring is compressed
• only when spring is stretched
• when spring is neither stretched nor compressed.

Solution

It increases in both cases as long as there is a deformation, whether positive or negative.

Q25. A force is conservative if

• the sum of the initial forces equals the final forces
• a constant force acts on the system
• work done over a closed path is zero
• work done for every path is zero

Solution

A force is conservative if the work done over a closed path is zero, as it depends only on the initial and final positions.

Q26. From a waterfall, water is falling at the rate of 100 kg/s on the blades of a turbine. If the height of fall is 100 m, the power delivered to the turbine is

• 100 kW
• 10 kW
• 1 kW
• 100 W

Solution

Power = work done / time taken or P = mgh / t P = (m/t) gh = 100 x 10 x 100 = 100 kW

Q27. Work done by or against a conservative force in a round trip is

• Maximum
• Minimum
• Zero
• May be maximum or zero

Solution

Work done by or against a conservative force in a round trip is zero

Q28. Reema and Rita are two identical twins (with same mass). To climb a tree up to same level, Reema takes 30 seconds whereas Rita takes 55 seconds. (i) Who did more work? (ii) Who used more power?

• Reema, Rita
• Rita, Reema
• Both, Rita
• Both, Reema

Solution

(A) Both did the same amount of work, that is, mgh. This is because their mass and the height to which they climb are same. (B) Power is defined by the amount of work done per unit time. So, the one who took less time used more power. Hence Reema used more power.

Q29. An astronomer has total weight of 80 kg. On reaching moon, he climbs up 10 m to enter his aircraft by the ladder. His gravitational potential energy is increased by 1000 J. The value of the gravitational acceleration on the moon is

• 1.25 N/kg
• 2 N/kg
• 2.25 kg
• 2.22 kg

Solution

Change in Gravitational Potential Energy = mass x acceleration due to gravity x change in height 1000 J = 80 kg x g x 10 m

Q30. A person A pushes a body of 5 kg placed on a rough surface of co-efficient of friction 0.3 by a distance of 4 m in 15 seconds. Another person B pushes the body of 7 kg on same surface by a distance of 3 m in the same time. Who has more energy and power?

• A
• B
• Both A and B have developed equal power but B has more energy
• Both A and B have developed equal power but A has more energy

Solution

Person A: mass of body is m = 5 kg Co-efficient of friction is μ = 0.3 Therefore, Force of friction is F = μmg = 0.3 x 5 x 10 = 15 N Displacement is s = 4 m Hence, Work done is W = 15 x 4 = 60 J Time taken is t = 15 s Hence, Power is P = 60/15 = 4 W Person B: mass of body is m = 7 kg Co-efficient of friction is μ = 0.3 Force of friction is F = μmg = 0.3 x 7 x 10 = 21 N Displacement is s = 3 m Hence, Work done is W = 21 x 3 = 63 J Time taken is t = 15 s Hence, Power is P = 63/15 = 4.2 W Thus, person B has more energy and power.

Q31. A shell, in its flight explodes into five unequal parts. Which of the following is conserved?

• Momentum
• Kinetic energy
• Potential energy
• Both potential energy and kinetic energy.

Solution

From the law of conservation of linear momentum, momentum will be conserved under the effect of zero external force.

Q32. If you drop a rubber ball from rest from a height of 3 m, what is the maximum height to which it will bounce back in the presence of air?

• = 3 m
• > 3 m
• 4 m
• < 3 m

Solution

To go higher, it would require a higher potential energy than when it started. For that an external work has to be done to add energy to it. Since here no such work is done so the ball won't go higher. Also the ball won't bounce as high as starting point as some energy is lost due to air resistance and heat when it bounces from the ground.

Q33. For a varying force work done can be expressed as a

• definite integral of force over displacement
• differentiation of force with displacement
• product of force and displacement
• force divided by the displacement

Solution

Q34. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

• 44 %    
• 50 %
• 56 %

Solution

Q35. A man A of mass 80 kg runs up a staircase in 12 seconds.  Another man of mass 60 kg runs up the same staircase in 11 seconds. The ratio of powers of A and B is :

• 11 : 12
• 11 : 9
• 12 : 11
• 9 : 11

Solution

Q36. A body is moved along a straight line path by a machine delivering constant power. The distance moved by the body in time t is proportional to:

• t^3/2
• t^1/4
• t^1/2
• t^3/4

Solution

Q37. When an electron is accelerated through a potential difference of 1 V, then, the energy acquired by the electron is

• 1 eV
• 1 watt
• 1 erg
• 1 joule

Solution

When an electron is accelerated through a potential difference of 1 V, then, the energy acquired by the electron is 1 eV.

Q38. Which of the following forces is non-conservative?

• spring force
• gravitational force
• frictional force
• none of the above

Solution

Work done by friction cannot be recovered, so work done by it over a closed path is not zero and it is non-conservative.

Q39. In an elastic collision in one dimension if a body A collides against the body B of equal mass at rest, then the body A will

• move with twice its initial velocity
• moves with the same velocity but in opposite direction.
• moves with the same velocity in the same direction.
• come to rest.

Solution

In an elastic collision in one dimension if a body A collides against the body B of equal mass at rest, then the body A will come to rest.

Q40. Raindrops fall on the earth with certain kinetic energy on the earth. From where do they get this energy?

• Gravitational Potential Energy
• Energy between molecules of water
• Chemical Energy
• Heat Energy