A uniform force of (2\(\hat { i }\)+\(\hat { j }\)) N acts on a particle of mass 1 kg. The particle displaces from position (3\(\hat { j }\)+\(\hat { k }\)) m to (5\(\hat { i }\)+3\(\hat { j }\)) m. The work done by the force on the particle is

(a)

9 J

(b)

6 J

(c)

10 J

(d)

12 J

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

(a)

20 J

(b)

30 J

(c)

40 J

(d)

10 J

The coefficient of restitution e for a perfectly elastic collision is ______________.

(a)

1

(b)

0

(c)

\(\alpha\)

(d)

-1

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

(a)

always negative

(b)

zero

(c)

always positive

(d)

not defined

If the potential energy of the particle is \(\alpha -\frac { \beta }{ 2 } { x }^{ 2 }\), then force experienced by the particle is

(a)

F = \(\frac { \beta }{ 2 } { x }^{ 2 }\)

(b)

F = βx

(c)

F = -βx

(d)

F = -\(\frac { \beta }{ 2 } { x }^{ 2 }\)

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)

\(\frac{2}{3}\)k

(b)

\(\frac{3}{2}\)k

(c)

3k

(d)

6k

A cricket ball falls from a height of 40 m. What is the velocity with which the ball hits the ground?

(a)

40 m/s

(b)

20 m/s

(c)

16 m/s

(d)

28 m/s

A particles moves along x-axis from x = 0 to x = 7m under the influence of a force given by f(x) = 12-2x+3x² then the workdone is__________________

(a)

205 J

(b)

390 J

(c)

378 J

(d)

291 J

A ball bounces to 75% of its original height. Calculate the mechanical energy lost in each bounce _________________.

(a)

0.40

(b)

0.35

(c)

0.25

(d)

0.20

Which one of the following is not the unit of energy?

(a)

joule

(b)

Nm

(c)

kW

(d)

kWh

When a body falls freely towards the earth, then its T.E. ______________.

(a)

increases

(b)

decreases

(c)

remains constant

(d)

first increases and then decreases

A boy is carrying a school bag of 5 kg mass on his back and moves 100 m on a levelled road. The work done against the gravitational force is ____________ (g = 10 ms^-1)

(a)

5J

(b)

500J

(c)

0.5J

(d)

zero

A simple pendulum hanging freely and at rest vertical because in that position ______________.

(a)

Kinetic Energy is zero

(b)

Kinetic Energy is minimum

(c)

Potential Energy is zero

(d)

Potential Energy is minimum

A ball whose Kinetic Energy is E is projected at an angle of 45° to the horizontal. The kinetic energy of the ball at the highest point of its flight will be _____________.

(a)

E

(b)

\(\frac{E}{\sqrt2}\)

(c)

\(\frac{E}{2}\)

(d)

zero

A gun of mass M fires a bullet of mass m with maximum speed v. G.T. m < M. The kinetic energy of the gun will be ______________.

(a)

\(\frac{1}{2}\)mv²

(b)

\(\frac{1}{2}\)Mv²

(c)

more than \(\frac{1}{2}\)mv²

(d)

less than\(\frac{1}{2}\)mv²

Two bodies of masses m and 4m are moving with equal kinetic energies. The ratio of their linear momenta is _____________.

(a)

1 : 2

(b)

1 : 4

(c)

4: 1

(d)

1: 1

A shell, in flight explodes into four unequal parts. Which is conserved?

(a)

potential energy

(b)

momentum

(c)

kinetic energy

(d)

both a and c

Power can be expressed as ______________.

(a)

\(\overrightarrow { F } .\overrightarrow { v } \)

(b)

\(\frac { 1 }{ 2 } \overrightarrow { F } .{ v }^{ 2 }\)

(c)

\(\overrightarrow { F } .{ t }\)

(d)

\(\overrightarrow { F } \times\overrightarrow { v } \)

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that ___________.

(a)

its kinetic energy is constant

(b)

its acceleration is constant

(c)

its velocity is constant

(d)

it moves in a straight line.

Two equal masses m₁ and m₂ moving along the same straight line with velocities +3 m/s and -5 m/s respectively collide elastically. Their velocities after the collision will be respectively _______________.

(a)

- 4 m/s and +4 m/s

(b)

+4 m/s for both

(c)

- 3 m/s and +5 m/s

(d)

- 5 m/s and + 3 m/s