A body of mass  $M$  is dropped from a height  $h$  on a sand floor. If the body penetrates $x\,\,cm$  into the sand, the average resistance offered by the sand of the body is

A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$  along the inclined calculate 

$(a)$ work done against gravity

$(b)$ work done against force of friction

$(c)$ increases in potential energy

$(d)$ increases in kinetic energy

$(e)$ work done by applied force

The kinetic energy acquired by a body of mass m is travelling some distance s, starting from rest under the actions of a constant force, is directly proportional to

A boy holds a uniform chain of length $2\,m$ which is kept on a smooth table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ………….. $\mathrm{J}$

A batsman hits a sixer and the ball touches the ground outside the cricket ground. Which of the following graph describes the variation of the cricket ball's vertical velocity $v$ with time between the time ${t_1}$ as it hits the bat and time $t_2$ when it touches the ground