A ladder is leaned against a smooth wall and  it is allowed to slip on a frictionless floor. Which figure represents trace of its centre of mass.

Assertion: : For a system of particles under central force field, the total angular momentum is conserved.

Reason:  The torque acting on such a system is 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

In an orbital motion, the angular momentum vector is

• along the radius vector

• parallel to the linear momentum

• in the orbital plane

• perpendicular to the orbital plane

The direction of the angular velocity vector is along

• the tangent to the circular path

• the inward radius

• the outward radius

• the axis of rotation

The motion of planets in the solar system is an example of the conservation of

• mass

• linear momentum

• angular momentum

• energy

Assertion: The earth is slowing down and as a result the moon is coming nearer to it.

Reason: The angular momentum of the earth moon system is not conserved.

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

• if both assertion and reason are true and the reason is not the correct explanation of the assertion

• if assertion is true but reason is false

• if both assertion and reason are false statements

Assertion: The length of the day is slowly increasing. 

Reason: The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.

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

• if both assertion and reason are true and the reason is not the correct explanation of the assertion

• if assertion is true but reason is false

• if both assertion and reason are false statements

The dimension of torque is

• [ M L^-2 ]

• [ M L^-1 T^-1 ]

• [ M L² T^-2 ]

• [ M L³ T^-3 ]

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

A conducting sphere of radius 1O cm is charged with 10 μC. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the spheres are separated, then surface density of charges on the spheres will be in the ratio of

• 1 : 4

• 1 : 2

• 1 : 3

• 1 : 1