The dimension of torque is

• [ M L^-2 ]

• [ M L^-1 T^-1 ]

• [ M L² T^-2 ]

• [ M L³ T^-3 ]

If vectors  $\overrightarrow{\mathrm{P}} = \mathrm{a}\hat{\mathrm{i}} + \mathrm{a}\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$  and  $\overrightarrow{\mathrm{Q}} = \mathrm{a}\hat{\mathrm{i}} - 2\hat{\mathrm{j}} - \hat{\mathrm{k}}$ are perpendicular to each other, then the positive value of  a  is

• 3

• 1

• 2

• 0

Three different objects  m₁ , m₂ and  m₃ to fall from rest and from the same point O along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of

• m₁ : m₂ : m₃

• 1 : 1 : 1

• m₁ : 2 m₂ : 3m₃

• $\frac{1}{{\mathrm{m}}_1} : \frac{1}{{\mathrm{m}}_2} : \frac{1}{{\mathrm{m}}_3}$

A particle starts from rest and has an acceleration  of 2 m/s² for  10 sec. After that, it travels for 30 sec with constant speed and then undergoes a retardation of 4 m/s²  and comes back to rest. The total distance covered by the particle is

• 650 m

• 750 m

• 700 m

• 800 m

Hubble's law is related with

• comet

• speed of galaxy

• black hole

• planetary motion

At the uppermost point of a projectile, its velocity and acceleration are at an angle of

• 0^°

• 90^°

• ^45°

• 180^°

The kinetic energy of a body becomes four times its initial value. The new linear momentum will be

• same as the initial value

• four times the initial value

• twice of the initial value

• eight times of the initial value

The angular momentum of a moving body remains constant if

• net external force is applied

• net external torque is applied

• net pressure is applied

• net external torque is not applied

The force of gravitation is

• repulsive

• conservative

• electrostatic

• non-conservative

Kepler's second law is based on

• Newton's first law

• special theory of relativity

• Newton's second law

• Conservation of angular momentum