Which of the following is not correct?

(1)  Force of friction is non-conservative.

(2)  If R is the horizontal range of an oblique the projectile, then the kinetic energy of the projectile is minimum after covering a horizontal the distance of R/2 considering air resistance.

(3)  Viscous force is a non-conservative force.

(4)  Work done in stretching a spring successively by length x from natural length are in the ratio 1:3.

One sphere collides with another sphere of double its mass. While heavier mass was at rest initially. The ratio of their respective speeds after the collision will be (Coefficient of restitution = e)

1.  $\frac{1 - 2\mathrm{e}}{1 - \mathrm{e}}$

2.  $\frac{1 - 2\mathrm{e}}{1 + \mathrm{e}}$

3.  $\frac{1 - \mathrm{e}}{1 + 2\mathrm{e}}$

4.  $\frac{1 + 2\mathrm{e}}{1 - \mathrm{e}}$

A particle of mass ${\mathrm{m}}_1$ makes an elastic, one-dimensional collision with another stationary particle of mass ${\mathrm{m}}_2$. The fraction of kinetic energy of ${\mathrm{m}}_1$ carried away by ${\mathrm{m}}_2$ is

1.  $\frac{{\mathrm{m}}_1^2}{{\mathrm{m}}_2^2}$

2.  ${\left(\frac{{\mathrm{m}}_1^2}{{\mathrm{m}}_2^2}\right)}^{-1}$

3.  $\frac{{\mathrm{m}}_1 - {\mathrm{m}}_2}{{\left({\mathrm{m}}_1 + {\mathrm{m}}_2\right)}^2}$

4.  $\frac{4{\mathrm{m}}_1{\mathrm{m}}_2}{{\left({\mathrm{m}}_1 + {\mathrm{m}}_2\right)}^2}$

The potential energy \(\mathrm{U}\) of a system is given by $\mathrm{U}=$ $\mathrm{A}$ $-$ ${\mathrm{Bx}}^2$ (where \(\mathrm{x}\) is the position of its particle and \(\mathrm{A},\) \(\mathrm{B}\) are constants). The magnitude of the force acting on the particle is:
1. constant

2. proportional to \(\mathrm{x}\)

3. proportional to ${\mathrm{x}}^2$

4. proportional to $\left(\frac{1}{\mathrm{x}}\right)$

A person-1 stands on an elevator moving with an initial velocity of 'v' & upward acceleration 'a'. Another person-2 of the same mass m as person-1 is standing on the same elevator. The work done by the lift on the person-1 as observed by person-2 in time 't' is:

1.  $\mathrm{m}\left(\mathrm{g}\right)$ $+$ $\mathrm{a}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

2.  $-\mathrm{mg}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

3.  0

4.  $\mathrm{ma}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

If a body of mass 2 kg is moved in the conservative field from point A to B in three different paths, then work done will be

(1)  ${\mathrm{W}}_{\mathrm{I}} < {\mathrm{W}}_{\mathrm{II}} < {\mathrm{W}}_{\mathrm{III}}$

(2)  ${\mathrm{W}}_{\mathrm{I}} > {\mathrm{W}}_{\mathrm{II}} > {\mathrm{W}}_{\mathrm{III}}$

(3)  ${\mathrm{W}}_{\mathrm{I}} = {\mathrm{W}}_{\mathrm{II}} = {\mathrm{W}}_{\mathrm{III}}$

(4)  ${\mathrm{W}}_{\mathrm{I}} > {\mathrm{W}}_{\mathrm{II}} = {\mathrm{W}}_{\mathrm{III}}$

Two pendulum bobs A and B of mass m and 2m respectively are simultaneously released from a height H above the lowest point, making an elastic collision at the lowest point. If after the first collision A and B rise to heights ${\mathrm{h}}_1 \mathrm{and} {\mathrm{h}}_2$ respectively, then ${\mathrm{h}}_1+2{\mathrm{h}}_2$ is:

1.  3H

2.  H

3.  $\frac{\mathrm{H}}{3}$

4.  $\frac{2\mathrm{H}}{3}$

Two particles moving initially in the same direction undergo a one-dimensional elastic collision. Their relative velocities before and after the collision are ${\overrightarrow{\mathrm{v}}}_1 \mathrm{and} {\overrightarrow{\mathrm{v}}}_2$. Which of the following is not correct?

1.  $\left|{\overrightarrow{\mathrm{v}}}_1\right| = \left|{\overrightarrow{v}}_2\right|$

2.  ${\overrightarrow{\mathrm{v}}}_1 = -{\overrightarrow{v}}_2$ only is the two are of equal mass

3.  ${\overrightarrow{\mathrm{v}}}_1.{\overrightarrow{v}}_2 = -{\left|{\overrightarrow{v}}_1\right|}^2$

4.  ${\overrightarrow{\mathrm{v}}}_1.{\overrightarrow{v}}_2 = -{\left|{\overrightarrow{v}}_2\right|}^2$

A particle is moving along the x-axis under a conservative force and its potential energy U varies with x co-ordinate as shown in the figure. Then force is positive at:

(1)  A

(2)  C, D 

(3)  B

(4)  D, E

The following are three graphs of the magnitude of force F versus time t for a body involved in a collision.

Then the relation between the magnitude of impulse on the body in these cases is best represented by

(1)  a > b > c

(2)  a = b = c

(3)  b > a > c

(4)  c > a < b