# A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere Option 1) total kinetic energy is conserved Option 2) angular momentum of the sphere about the point of contact with the plane is conserved Option 3) only the rotational kinetic energy about the centre of mass is conserved. Option 4) angular momentum about the centre of mass is conserved.

As we discussedin

Law of conservation of angular moment -

$\vec{\tau }= \frac{\vec{dL}}{{dt}}$

- wherein

If net torque is zero

i.e. $\frac{\vec{dL}}{{dt}}= 0$

$\vec{L}= constant$

angular momentum is conserved only when external torque is zero .

Angular momintum absent the pont of contact with the plane remains conseved.

Option 1)

total kinetic energy is conserved

incorrect

Option 2)

angular momentum of the sphere about the point of contact with the plane is conserved

correct

Option 3)

only the rotational kinetic energy about the centre of mass is conserved.

incorrect

Option 4)

angular momentum about the centre of mass is conserved.

incorrect

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