A particle is moving in a circular path of radius $a$, with a constant velocity $v$ as shown in the figure. The centre of circle is marked by 'C'. The angular momentum from the origin O can be written as:
(1) $va(1+\cos 2\theta)$
(2) $va(1+\cos\theta)$
(3) $va\cos 2\theta$
(4) $va$

A particle is moving along a circular path with a constant speed of $10 \mathrm {~ms} ^ { - 1 }$. What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60 ^ { \circ }$ around the centre of the circle?
(1) $10 \sqrt { 3 } \mathrm {~m} / \mathrm { s }$
(2) zero
(3) $10 \sqrt { 2 } \mathrm {~m} / \mathrm { s }$
(4) $10 \mathrm {~m} / \mathrm { s }$