The $50\, kg$ homogeneous smooth sphere rests on the $30^o$ incline $A$ and bears against the smooth vertical wall $B$. Calculate the contact force at $A$
$\frac{{500}}{{\sqrt 3 }}\,N$
$500\,N$
$\frac{{1000}}{{\sqrt 3 }}\,N$
$1000\,N$
A block placed on a rough inclined plane of inclination $\left(\theta=30^{\circ}\right)$ can just be pushed upwards by applying a force " $F$ " as shown. If the angle of inclination of the inclined plane is increased to $\left(\theta=60^{\circ}\right)$, the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is
A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$ , the centre of mass of the system (trolley + child) will move with a speed
Objects $A$ and $B$ each of mass $m$ are connected by light inextensible cord. They are constrained to move on a frictionless ring in a vertical plane as shown in figure. The objects are released from rest at the positions shown. The tension in the cord just after release will be
A constant force $F$ is applied in horizontal direction as shown. Contact force between $M$ and $m$ is $N$ and between $m$ and $M ^{\prime}$ is $N ^{\prime}$ then
Two masses of $10\,kg$ and $20\,kg$ respectively are connected by a massless spring as shown in figure. A force of $200\,N$ acts on the $20\,kg$ mass at the instant when the $10\,kg$ mass has an acceleration of $12\,ms ^{-2}$ towards right, the aceleration of the $20\,kg$ mass is: