Center of Mass Momentum and Collision

The force $'F'$ acting on a particle of mass $'m'$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8s$ is:

Point masses $m_{1}$ and $m_{2}$ are placed at the opposite ends of rigid rod of length $\text{L}$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $\text{L}$…

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R), Assertion (A): When a fire cracker (rocket) explodes in mid air, its fragments fly in such a way that they…

A moving block having mass $m,$ collides with another stationary block having mass $4m.$ The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v,$ then the value of…

The position of an object having mass $0.1$ kg as a function of time $t$ is given as $\vec{r} = \left(10t^2\hat{i} + 5t^3\hat{j}\right)$ m. At $t = 1$ s, which of the following statements are correct? A. The linear…

The centre of mass of a solid hemisphere of radius$8\mathrm{cm}$is$x\mathrm{cm}$from the centre of the flat surface. Then value of$x$is

A ball is dropped from a height of $20m$. If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ______ $m$?

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

A body of mass$M$at rest explodes into three pieces, in the ratio of masses$1:1:2$. Two smaller pieces fly off perpendicular to each other with velocities of$30ms^{-1}$and$40ms^{-1}$respectively. The velocity of the…

The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass$4kg$. (The coordinates of the same are shown in the figure) are:

Distance of the centre of mass of a solid uniform cone from its vertex is$z_{0}$. If the radius of its base is$R$and its height is$h$then$z_{0}$is equal to:

Two identical bodies $A$ and $B$ of equal masses have initial velocities $\vec{v_1} = 4\hat{i}$ m/s and $\vec{v_2} = 4\hat{j}$ m/s respectively. The body $A$ has acceleration $\vec{a_1} = 6\hat{i} + 6\hat{j}$ m/s$^2$…