Assertion:  Value of radius of gyration of a body depends on axis of rotation. 

Reason:  Radius of gyration is root mean square distance of particle of the body from the axis of rotation.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  A judo fighter in order to throw his opponent on to the mat tries to initially bend his opponent and then rotate him around his hip. 

Reason:  As the mass of opponent is brought closer to the fighter's hip, the force required to throw the opponent is reduced.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is

• a

• 2a

• 3a

• none of these

Assertion:  A body subject to three concurrent forces may be in equilibrium. 

Reason: For equilibrium, the sum of all the concurrent forces acting at a point should be zero.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

A dipole of dipole moment 'p' is placed in non-uniform electric field along x-axis. Electric field is increasing at the rate of 1 V m^-1 then the force on dipole is

• 0

• 2p

• p/2

• p

Dimensional formula of angular momentum is

• [ M L² T^-1 ]

• [ M² L² T^-2 ]

• [ M L² T^-3 ]

• [ M L T^-1 ]

Relation between magnetic moment and angular velocity is

• M ∝ ω

• M ∝ ω²

• M ∝ $\sqrt{\mathrm{\omega }}$

• None of these

Given that force  $\left( 5\hat{\mathrm{i}} + 7\hat{\mathrm{j}} - 3\hat{\mathrm{k}} \right)$N  acts on a particle at position  $\left( \hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}} \right)$m. Find torque of this force on the particle about origin.

• $4\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 2\hat{\mathrm{k}}$

• $2\hat{\mathrm{i}} - 3\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$

• $5\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

• $6\hat{\mathrm{i}} - 4\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$

Assertion: Moment of inertia is always constant. 

Reason:  Angular moment is conserved that is why moment of inertia is constant.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  Centre of mass of a system does not move under the action of internal forces. 

Reason: Internal forces are non conservative forces.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.