For the given system,which of the following relations holds between $T_1$,$T_2$,and $T_3$?

What is the ratio of the accelerations of both systems?

$A$ car is moving with uniform velocity on a rough horizontal road. Therefore,according to Newton's first law of motion,

What force should be applied on the wedge so that the block over it does not move? (All surfaces are smooth)

An object of mass $10 \,kg$ is projected from the ground with a speed of $40 \,m/s$ at an angle of $60^{\circ}$ with the horizontal. The rate of change of momentum of the object one second after projection in $SI$ units is ........ [Take $g = 9.8 \,m/s^2$]

$A$ particle of mass $m=1 \ kg$ moves in the $xy$-plane. The force on it at time $t$ is $F(t)=[2 \sin (\alpha t) \hat{i}+3 \cos (\alpha t) \hat{j}] \ N$,where $\alpha=1 \ s^{-1}$. At time $t=0$,the particle is at rest at the origin. Calculate the magnitude of its position vector $r$ (in $m$) and velocity vector $v$ (in $m/s$) at time $t=\frac{\pi}{2} \ s$.