A boy of mass $4\, kg$ is standing on a piece of wood having mass $5 \,kg$. If the coefficient of friction between the wood and the floor is $0.5,$ the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ......$N.$(Round off to the Nearest Integer) [Take $g=10 \,ms ^{-2}$ ]

For the given figure, if block remains in equilibrium position then find frictional force between block and wall ........ $N$

A man balances himself in a horizontal position by pushing his hands and feet against two parallel walls. His centre of mass lies midway between the walls. The coefficients of friction at the walls are equal. Which of the following is not correct?

A block of mass $5\, kg$ is kept on a rough horizontal floor. It is given a velocity $33\, m/s$ towards right. A force of $20\sqrt {2\,} \,N$ continuously acts on the block as shown in the figure. If the coefficient of friction between block and floor is $0.5$ the velocity of block after $3\, seconds$ is ........ $m/s$  ($g = 10\, m/s^2$)

A $1.0 kg$ block of wood sits on top of an identical block of wood, which sits on top of a flat level table made of plastic. The coefficient of static friction between the wood surfaces is $\mu_1$, and the coefficient of static friction between the wood and plastic is $\mu_2$. Ahorizontal force $F$ is applied to the top block only, and this force is increased until the top block starts to move. The bottom block will move with the top block if and only if

$Assertion$ : Angle of repose is equal to the angle of limiting friction.
$Reason$ : When the body is just at the point of motion, the force of friction in this stage is called limiting friction.