A man is at a distance of  6 m from a bus. The bus begins to move with a constant acceleration of 3ms.In order to catch the bus, the minimum speed with which the man should run towards the bus is

• 2 m s^-1

• 4 m s^-1

• 6 m s^-1

• 8 m s^-1

If  $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ are non-zero vectors which obey the relation  $\left| \overrightarrow{\mathrm{A}} + \overrightarrow{\mathrm{B}} \right| = \left| \overrightarrow{\mathrm{A}} - \overrightarrow{\mathrm{B}} \right|$, then the angle between them is

• 0^o

• 60^o

• 90^o

• 120^o

Time period of pendulum, on a satellite orbiting the earth, is

• $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\pi }$}\right.$

• zero

• $\mathrm{\pi }$

• infinity

A gun of mass 10 kg fires 4 bullets per second. The mass of each bullet is 20 g and the velocity of the bullet when it leaves the gun is 300 m s^-1. The force required to hold the gun when firing is

• 6 N

• 8 N

• 24 N

• 240 N

A stone of mass 0.3 kg attached to a 1.5 m long string is whirled around in a horizontal circle at a speed of 6 m s^-1 The tension in the string is

• 10 N

• 20 N

• 7.2 N

• 30 N

6.

A ball is dropped from the top of a building 100 m high. At the same instant another ball is thrown upwards with a velocity of 40 m/s from the bottom of the building. The two balls will meet after

• 3 s

• 2 s

• 2.5 s

• 5 s

If the linear momentum is increased by 50%, then kinetic energy will increase by

• 0 %

• 100 %

• 125 %

• 25 %

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to transfer it from a circular orbit of radius R, to another of radius R₂ (R₂ > R₁ ) is

• GmM $\left(\frac{1}{{\mathrm{R}}_1^2} - \frac{1}{{\mathrm{R}}_2^2}\right)$

• GmM $\left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• 2 GmM $\left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• $\frac{1}{2}$ GmM $\left(\frac{1}{{\mathrm{R}}_1}- \frac{1}{{\mathrm{R}}_2}\right)$

A sphere of mass 10 kg and radius 0.5 m rotates about a tangent. The moment of inertia of the sphere is

• 5 kg m²

• 2.7 kg m²

• 3.5 kg m²

• 4.5 kg m²

A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled (x)?