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 $\text{L}$…

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 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:

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…

Consider two blocks A and B of masses $m_1=10 \mathrm{~kg}$ and $m_2=5 \mathrm{~kg}$ that are placed on a frictionless table. The block A moves with a constant speed $v=3 \mathrm{~m} / \mathrm{s}$ towards the block B…

A rod of length 5 L is bent right angle keeping one side length as 2 L. The position of the centre of mass of the system: (Consider $\mathrm{L}=10 \mathrm{~cm}$)

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…

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of$5$times its mass? (Assume the collision to be head-on elastic collision)

An object of mass$m_{1}$collides with another object of mass$m_{2}$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses$m_{2}:m_{1}$is :

A large block of wood of mass$M=5.99kg$is hanging from two long massless cords. A bullet of mass$m=10g$is fired into the block and gets embedded in it. The (block$+$ bullet) then swing upwards, their center of mass…

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: