Center of Mass Momentum and Collision

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 $\text{L}$…

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…

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 particle of mass $\text{m}$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v.$ If the collision is perfectly inelastic, the percentage loss…

Blocks of masses $\text{m},2\text{m},4\text{m}$ and $8\text{m}$ are arranged in a line of a frictionless floor. Another block of mass $m$ , moving with speed $\upsilon\,$ along the same line (see figure) collides with…

A circular hole of radius $\left(\frac{a}{2}\right)$ is cut out of a circular disc of radius $a$ as shown in figure. The centroid of the remaining circular portion with respect to point $O$ will be:

A body of mass $M$moving at speed $V_{0}$ collides elastically with a mass $m$at rest. After the collision, the two masses move at angles $\theta\,_{1}$ and $\theta\,_{2}$ with respect to the initial direction of motion…

The position vector of the center of mass $\vec{r}_{\mathrm{cm}}$of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

A particle of mass $m$ is moving with speed $2\text{v}$ and collides with a mass $2m$ moving with speed $\text{v}$ in the same direction. After the collision, the first mass is stopped completely while the second one…

Consider a uniform rod of mass $M=4m$ and length $l$ pivoted about its centre. A mass $m$ moving with velocity $v$ making angle $\theta\,=\frac{\pi\,}{4}$ to the rod's long axis collides with one end of the rod and…

A rod of length $l$ has non-uniform linear mass density given by $\rho\,\left(x\right)=a+b\left(\frac{x}{l}\right)^{2},$ where $a$ and $b$ are constants and $0\leq\,x\leq\,l$ The value of $x$ for the centre of mass of…

Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure.