Two spherical shells one which is placed in air has constant charge Q; and the other which is placed in a medium of dielectric constant K has a charge Q;­ The ratio of forces between the shell is:

• K : 1

• 1 : K

• K² : 1

• 1 : K²

A block of mass 1 kg is placed on the wall under a force F. If coefficient of friction ($\mathrm{\mu }$) is 0.5, then minimum value of force applied is :

• 9.8 N

• 49 N

• 19.6 N

• 1.96 N

Mass of a planet is 10 times that of earth and radius is 2 times that of earth. If at the earth, the escape velocity of a satellite is V_es(e), then escape. velocity at the planet is :

• $\sqrt{5}$v_es(e)

• 5v_es(e)

• 2$\sqrt{5}$ v_es(e)

• 10 v_es(e)

A car and a container, moving with equal kinetic energies are stopped by applying a negative acceleration. Then

• container will move less distance before being stopped

• both will become stationary after moving some distance

• car will move less distance before being stopped

• none of the above

The mass of a solid sphere is 2 kg and radius is 10 cm. Sphere, tied to one end of 1 m long string, is rotated at a rate of 10 rad/sec. The rotational kinetic energy of sphere is :

• 121.4 J

• 18.5 J

• 15.2 J

• 22.0 J

A rocket is accelerated with speed v= 2$\sqrt{g{R}_e}$, near earth surface and then it moves upward. At far distance from the earth surface, the speed of the rocket will
be:

• $\sqrt{g{R}_e/2}$

• $\sqrt{g{R}_e}$

• (2-$\sqrt{2}$)$\sqrt{g{R}_e}$

• $\sqrt{2g{R}_e}$

In the rotational motion, different particles of the body have :

• both linear and angular velocities equal

• linear velocities equal but different angular velocities

• angular velocities equal but different linear velocities

• both linear and angular velocity different

A car covers 2/5 of a certain distance with speed v₁ and rest 3/5 part with velocity v_2. The average speed of the car is :

• $\frac{1}{2}\sqrt{{\mathrm{v}}_1{\mathrm{v}}_2}$

• $\frac{5{\mathrm{v}}_1{\mathrm{v}}_2}{3{\mathrm{v}}_1+2{\mathrm{v}}_2}$

• $\frac{2{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1+{\mathrm{v}}_2}$

• $\frac{{\mathrm{v}}_1+{\mathrm{v}}_2}{2}$

The momentum of two masses m₁ and m₂ are same. The ratio of their kinetic energies E₁ and E₂ is

• $\sqrt{{\mathrm{m}}_1} : \sqrt{{\mathrm{m}}_2}$

• m₁ : m₂

• m₂ : m₁

• m₁² : m₂² 

A car is moving with speed 30 m/s on a circular path of radius 500 m. If its speed is increasing at a rate of 5m/s², then resultant acceleration at that instant is

• 6.83 m/s²

• 8 m/s²

• 5.31 m/s²

• 4 m/s²