A particle of mass m moving with a velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$ establishing a contact with it for extremely small time $T$. Their force of contact increases from zero to $F_0$ linearly in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$ and decreases linearly from $F_0$ to zero in further time $\frac{T}{4}$ as shown. The magnitude possessed by $F_0$ is
$\frac{{mu}}{T}$
$\frac{{2mu}}{T}$
$\frac{{4mu}}{{3T}}$
$\frac{{3mu}}{{4T}}$
The time in which a force of $2 \,N$ produces a change of momentum of $0.4\,kg - m{s^{ - 1}}$ in the body is ......... $\sec$
Figure shows the position-time graph of a particle of mass $4 \,kg$. What is the
$(a)$ force on the particle for $t\, <\, 0, t \,> \,4\; s, 0 \,<\, t \,< \,4\; s$?
$(b)$ impulse at $t=0$ and $t=4 \;s ?$ (Consider one-dimensional motion only).
$100 \,g$ of a iron ball having velocity $10 \,m/s$ collides with a wall at an angle ${30^o}$ and rebounds with the same angle. If the period of contact between the ball and wall is $0.1 \,second$, then the force experienced by the ball is ............. $\mathrm{N}$
Displacement of a particle of mass $2\, kg$ moving in a straight line varies with time as $s = (2t^3 + 2)\, m$. Impulse of the force acting on the particle over a time interval between $t = 0$ and $t = 1\, s$ is .......... $N-s$
Two billiard balls of equal mass $30 \,{g}$ strike a rigid wall with same speed of $108\, {kmph}$ (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball $'a'$ and ball $'b'$ by the wall along $'X'$ direction is :