For the path wxyz in a conservative field, the amount of work done in carrying a body from w to x and from x to y and from y to z are 2 J. 4 J and 6 J respectively. The work done in carrying the body from w to z will be

                            

(1)  12 J

(2)  2 J

(3)  4 J

(4)  6

20 J of work is done to increase the length of a light spring by 1 cm from its natural length. Work done in increasing its length further by 1 cm is:

(1)  20 J

(2)  40 J

(3)  30 J

(4)  60 J

The work-energy theorem is the scalar form of Newton's

(1)  The first law of motion

(2)  The second law of motion

(3)  Third law of motion

(4)  All of these

A pendulum bob is made to move along a vertical circle such that it passes the highest point with critical speed. The ratio of centripetal and tangential acceleration when the string becomes horizontal is

(1)  1: 3

(2)  3: 1

(3)  1: 9

(4)  9: 1

A block of mass m is given a speed v when the spring of constant k is in its natural length as shown in the figure. The remaining kinetic energy of the block when spring is compressed by half of the maximum compression is:

(1)  25%

(2)  50%

(3)  75%

(4)  Any value of less than 50%

A body of mass m moving at a certain speed suffers a perfectly inelastic collision with a body of mass M at rest. The ratio of the final kinetic energy of the system to the initial kinetic energy will be:

A shell fired from a cannon explodes in mid-air. It's total

(1)  Linear momentum is not conserved

(2)  Linear momentum is conserved

(3)  Kinetic energy is conserved

(4)  Potential energy is conserved

A constant force is applied on a body of mass 2 kg to give it a displacement $\mathrm{s} = \frac{1}{2}{\mathrm{t}}^2$. Work done by agent applying the force up to time t = 3 s is

(1)  3 J

(2)  9 J

(3)  18 J

(4)  2 J

A particle of mass 10 kg is moving with a velocity of $10\sqrt{x}$ m/s, where x is displacement. The work done by net force during the displacement of the particle from x = 4 m to x = 9 m is:

(1)  1250 J

(2)  1000

(3)  3500 J

(4)  2500 J

Two bodies A and B of mass m and 2m respectively are placed on a smooth floor as shown. They are connected by a spring of constant k. If a third body C of mass m moves with a velocity ${\mathrm{v}}_0$ along the line joining A and B and collides head-on elastically with A, then speed of A at the instant of maximum compression is

1.  ${\mathrm{v}}_0$

2.  $\frac{{\mathrm{v}}_0}{2}$

3.  $\frac{{\mathrm{v}}_0}{4}$

4.  $\frac{{\mathrm{v}}_0}{3}$