A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ -direction. Its speed $v(t)$ is depicted by which of the following curves ?
A block of mass $1\, kg$ is at rest on a horizontal table. The coefficient of static friction between the block and the table is $0.5.$ The magnitude of the force acting upwards at an angle of $60^o$ from the horizontal that will just start the block moving is
A truck starting from rest moves with an acceleration of $5 m/s^2$ for $1 sec$ and then moves with constant velocity. The velocity $w.r.t$ ground $v/s$ time graph for block in truck is ( Assume that block does not fall off the truck)
A lift is moving downwards with an acceleration equal to acceleration due to gravity. $A$ body of mass $M$ kept on the floor of the lift is pulled horizontally. If the coefficient of friction is $\mu $, then the frictional resistance offered by the body is
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 $g=10 \,ms ^{-2}$ ]
A horizontal force $12 \,N$ pushes a block weighing $1/2\, kg$ against a vertical wall. The coefficient of static friction between the wall and the block is $0.5$ and the coefficient of kinetic friction is $0.35.$ Assuming that the block is not moving initially. Which one of the following choices is correct (Take $g = 10 \,m/s^2$)