$A$ particle moves in a circle of radius $R$,with a constant speed $v$. Then,during a time interval $t = \pi R / 3v$,which of the following is true?

$A$ particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When the particle moves from one point to a diametrically opposite point,its

$A$ particle performs uniform circular motion with an angular momentum $L$. If the frequency of the particle's motion is doubled and its kinetic energy is halved,then its angular momentum becomes

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta_1$ and $\theta_2$ respectively from the horizontal,and $v_1 \sin \theta_1 = v_2 \sin \theta_2$,then choose the incorrect statement.

Starting from the origin at time $t=0,$ with initial velocity $5 \hat{j} \, m/s,$ a particle moves in the $x-y$ plane with a constant acceleration of $(10 \hat{i} + 4 \hat{j}) \, m/s^2$. At time $t$,its coordinates are $(20 \, m, y_0 \, m)$. The values of $t$ and $y_0$ are respectively:

Read each statement below carefully and state,with reasons,if it is true or false:
$(a)$ The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
$(b)$ The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
$(c)$ The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.