Three masses of $16 \, kg$,$8 \, kg$,and $4 \, kg$ are placed in contact as shown in the figure. If a force of $140 \, N$ is applied on the $4 \, kg$ mass,then the force on the $16 \, kg$ mass will be ............ $N$.

$A$ trolley of mass $20 \ kg$ is attached to a block of mass $4 \ kg$ by a massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between the trolley and the surface is $0.02$,then the acceleration of the trolley and block system is (take $g=10 \ ms^{-2}$):- (in $ms^{-2}$)

$A$ car of mass $1000\,kg$ is moving at a speed of $30\,m/s.$ Brakes are applied to bring the car to rest. If the net retarding force is $5000\,N,$ the car comes to stop after travelling $d\,m$ in $t\,s.$ Then

Three solids of masses $m_1, m_2$ and $m_3$ are connected with weightless strings in succession and are placed on a frictionless table. If the mass $m_3$ is dragged with a force $T$,the tension in the string between $m_2$ and $m_3$ is

Two objects $A$ and $B$,each of mass $m$,are connected by a light inextensible string. They are restricted to move on a frictionless ring of radius $R$ in a vertical plane (as shown in the figure). The objects are released from rest at the position shown. Then,the tension in the cord just after release is

Two particles each of mass $m$ are moving in horizontal circles with the same angular speed $\omega$. If both strings are of the same length $l$,find the ratio of tension in the strings $\frac{T_1}{T_2}$.