A long block A of mass M is at rest on a smooth horizontal surface.  A small block B of mass M/2 is placed on A at one end and projected along A with same velocity v. The coefficient of friction between the block is μ. Then the acceleration of blocks A and B before reaching a common velocity will be respectively

• $\frac{\mathrm{\mu g}}{2} (\mathrm{towards} \mathrm{right}), \frac{\mathrm{\mu g}}{2} (\mathrm{towards} \mathrm{left})$

• $\mathrm{\mu g} (\mathrm{towards} \mathrm{right}), \mathrm{\mu g} (\mathrm{towards} \mathrm{left})$

• $\frac{\mathrm{ug}}{2} (\mathrm{towards} \mathrm{right}), \mathrm{\mu g} (\mathrm{towards} \mathrm{left})$

• $\mathrm{\mu g} (\mathrm{towards} \mathrm{right}), \frac{\mathrm{\mu g}}{2} (\mathrm{towards} \mathrm{left})$

A car of mass 1000 kg moves on a circular track of radius 20 m. If the coefficient of friction of 0.64. The maximum velocity with which the car can be moved is

• 11.2m/s

• 112m/s

• $\frac{0.64\times 20}{1000\times 100}\mathrm{m}/\mathrm{s}$

• $\frac{1000}{64\times 20}\mathrm{m}/\mathrm{s}$

The angle through which a cyclist bends when he covers a circular path of 34.3 m circumference in $\sqrt{22}$ sec is (g=9.8 m/s)

• 15⁰

• 30⁰

• 60⁰

• 45⁰

A body of mass 0.1 kg attains a velocity of 10 ms' in 0.1 sec. The force acting on the body is

• 10N

• 0.01N

• 0.1N

• 100N

A body is moving in a circular path with acceleration 'a'. If its velocity gets doubled, find the ratio of acceleration after and before the change 

• 1:4

• $\frac{1}{4}:1$

• 2:1

• 4:1

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. The speed of the system, will be

• 3v

• $\frac{\mathrm{v}}{2}$

• $\frac{\mathrm{v}}{3}$

• 2v

A cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?

• 2 s

• 4 s

• 1 s

• 6 s

158.

$\mathrm{Which} \mathrm{is} \mathrm{true} \mathrm{for} \mathrm{rolling} \mathrm{frictrion} \left( {\mathrm{\mu }}_{\mathrm{r} }\right), \mathrm{static} \mathrm{friction}\left( {\mathrm{\mu }}_{\mathrm{s}} \right) \mathrm{and} \mathrm{kinetic} \mathrm{friction} \left( {\mathrm{\mu }}_{\mathrm{k} }\right):$

• ${\mathrm{\mu }}_{\mathrm{s}} > {\mathrm{\mu }}_{\mathrm{k}} > {\mathrm{\mu }}_{\mathrm{r}}$

• ${\mathrm{\mu }}_{\mathrm{s}} < {\mathrm{\mu }}_{\mathrm{k}} < {\mathrm{\mu }}_{\mathrm{r}}$

• ${\mathrm{\mu }}_{\mathrm{s}} < {\mathrm{\mu }}_{\mathrm{k}} > {\mathrm{\mu }}_{\mathrm{r}}$

• ${\mathrm{\mu }}_{\mathrm{s}} > {\mathrm{\mu }}_{\mathrm{r} } > {\mathrm{\mu }}_{\mathrm{k}}$

Two weights w₁ and w₂ are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration g, then the tension in the string is :

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 ms'.The kinetic energy of the other mass is

• 256 J

• 486 J

• 524 J

• 324 J