Work, Energy and Power: Multiple choice questions with answers

1. A uniform force of (2iˆ+ ˆj) N acts on a particle of mass 1 kg. The particle displaces from position (3  ˆj + ˆk ) m to (5iˆ­+3ˆj) m. The work done by the force on the particle is

 

(a) 9 J

(b) 6 J

(c) 10 J

(d) 12 J

 

2. A ball of mass 1 kg and another of mass 2 kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of

 

(a) √2 : 1

(b) 1 : √2

(c) 2 : 1

(d) 1 : 2

 

3. A body of mass 1 kg is thrown upwards with a velocity 20 m s⁻¹. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?. (Take g= 10ms^-2 )

 

(a) 20 J

(b) 30 J

(c) 40 J

(d) 10 J

 

4. An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water ?.

 

a) ½ mv²

b) mv²

c) ½ mu²

d) mu²

 

5. A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

 

(a) mv²

(b) 3/2 mv²

(c) 2mv²

(d) 4mv²

 

6. The potential energy of a system increases, if work is done

 

(a) by the system against a conservative force

(b) by the system against a non-conservative force

(c) upon the system by a conservative force

(d) upon the system by a non-conservative force

 

7. What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?.

 

(a) √(2gR)

(b) √(3gR)

(c) √(5gR)

(d) √(gR)

 

8. The work done by the conservative force for a closed path is

 

(a) always negative

(b) zero

(c) always positive

(d) not defined

 

9. If the linear momentum of the object is increased by 0.1%, then the kinetic energy is increased by

 

(a) 0.1 %

(b) 0.2%

(c) 0.4%

(d) 0.01%

 

10. If the potential energy of the particle is ­α - β/2 x², then force experienced by the particle is

 

(a) F=β/2 x²

(b) F=βx

(c) F=-βx

(d) F=-β/2 x²

 

11. A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

 

(a) v

(b) v²

(c) v³

(d) v⁴

 

12. Two equal masses m₁ and m₂ are moving along the same straight line with velocities 5ms^-1 and -9ms^-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m₁ and m₂, respectively

 

(a) -4ms^-1 and 10 ms^-1

(b) 10ms^-1 and 0 ms^-1

(c) -9ms^-1 and 5 ms^-1

(d) 5 ms^-1 and 1 ms^-1

 

13. A particle is placed at the origin and a force F=kx  is acting on it (where k is a positive constant). If U(0)=0, the graph of U(x­) versus x will be (where U is the potential energy function)

Ans: c

 

14. A particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) =-kx+ax³.

Here, k and a are positive constants. For x ≥ 0, the functional form of the potential energy U(x) of the particle is

Ans: d

 

15. A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

 

(a) 2/3 k

(b) 3/2 k

(c) 3k

(d) 6k

 

Answers

1) c 2) d 3) a 4) a 5) b

6) a 7) c 8) b 9) b 10) c

11) c 12) c 13) c 14) d 15) b