## Important Questions on Centre of Mass

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

A block of mass $M$at rest on the floor is attached to a ball of mass $\frac{M}{2}$ via a light inextensible string of length $L$which passes over a light small frictionless pulley. The pulley is at a height of $0.6L$ from the floor. The ball is raised to a height of $\frac{L}{6}$and released (see figure). The speed of the block at the instant the string gets taut (not slack) will be

EASY

Physics>Mechanics>Centre of Mass>Impulse

A rigid ball of mass,$m$ strikes a rigid wall at ${60}^{o}$ and gets reflected without any loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

A carrom coin of radius $1.5\mathrm{cm}$and mass $5\mathrm{g}$strikes the side of the board at an angle $30\xb0$with respect to the normal. The coin stays in contact with the side for ${10}^{-3}\mathrm{s}$and rebounds at an angle of $45\xb0$with respect to the normal. The initial speed of the coin is $1{\mathrm{ms}}^{-1}$and its final speed is $0.7{\mathrm{ms}}^{-1}$. The average impulsive force on the coin in the normal direction is about

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

Physics>Mechanics>Centre of Mass>Impulse

Two billiard balls of equal mass $30\mathrm{g}$ strike a rigid wall with same speed of $108\mathrm{km}{\mathrm{h}}^{-1}$ (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:

EASY

Physics>Mechanics>Centre of Mass>Impulse

A time varying force acts on a ball of mass $100\mathrm{g}$for $2\mathrm{ms}$. The force versus time curve is shown below. If the initial speed of the ball is $10\mathrm{m}{\mathrm{s}}^{-1}$, then the speed of ball after $2\mathrm{ms}$is

EASY

Physics>Mechanics>Centre of Mass>Impulse

A ball of mass $3\mathrm{kg}$, moving with a speed of $100\mathrm{m}{\mathrm{s}}^{-1}$, strikes a wall at an angle $60\xb0$ (as shown in figure). The ball rebounds at the same speed and remains in contact with the wall for $0.2\mathrm{s}$; the force exerted by the ball on the wall is:

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

In Young's double slit experiment, the intensity of light at a point on the screen is $K$unit for path difference ${}^{\text{'}}\lambda ^{\text{'}}$. What would be the intensity at a point if path difference is $\frac{\lambda}{4}$

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

A bullet of$4\mathrm{g}$ mass is fired from a gun of mass $4\mathrm{kg}.$If the bullet moves with the muzzle speed of $50{\mathrm{ms}}^{1},$the impulse imparted to the gun and velocity of recoil of gun are

EASY

Physics>Mechanics>Centre of Mass>Impulse

Starting from rest, a car moves with a constant acceleration, and comes to a momentary stop with the same constant deceleration. Subsequently, it reverses its motion and returns to its original position in a similar manner. Which one of the following graphs of momentum $\left(p\right)$ versus time $\left(t\right)$ best describes the motion of the car?

EASY

Physics>Mechanics>Centre of Mass>Impulse

A batsman hits back a ball of mass $0.4\mathrm{kg}$straight in the direction of the bowler without changing its initial speed of $15{\mathrm{m}\mathrm{s}}^{-1}$. The impulse imparted to the ball is _____$\mathrm{N}\mathrm{s}$.

EASY

Physics>Mechanics>Centre of Mass>Impulse

The correct dimensional formula for impulse is given by

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

A particle having a mass $0.5\mathrm{kg}$ is projected under gravity with a speed of $98\mathrm{m}{\mathrm{sec}}^{-1}$ at an angle of $60\xb0$. The magnitude of the change in momentum (in $\mathrm{N}\mathrm{sec}$) of the particle after $10\mathrm{seconds}$ is $\left[g=9.8\mathrm{m}{\mathrm{s}}^{-2}\right]$

EASY

Physics>Mechanics>Centre of Mass>Impulse

In two different experiments, an object of mass $5\mathrm{kg}$ moving with a speed of $25{\mathrm{ms}}^{-1}$ hits two different walls and comes to rest within

(i) $3$ second, (ii) $5$ seconds, respectively.

Choose the correct option out of the following :

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

A ball of mass $0.15\mathrm{kg}$ is dropped from a height $10\mathrm{m}$strikes the ground and reboundsto the same height. The magnitude of impulse imparted to the ball is $\left(g=10\mathrm{m}{\mathrm{s}}^{-2}\right)$ nearly :

EASY

Physics>Mechanics>Centre of Mass>Impulse

Figure represents the position-time graph of a body of mass $4\mathrm{kg}$. Impulse $\left(\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}\right)$ imparted to the body at $t=0$is

MEDIUM

Physics>Mechanics>Centre of Mass>Impulse

The force $\u2018F\text{'}$ acting on a particle of mass $\u2018m\text{'}$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8\mathrm{s}$ is:

EASY

Physics>Mechanics>Centre of Mass>Impulse

A $2000\mathrm{kg}$rocket in free space expels $0.5\mathrm{kg}$of gas per second at exhaust velocity $400\mathrm{m}{\mathrm{s}}^{\u20131}$ for $5$ seconds. What is the increase in the speed of rocket in this time (assume time interval is too small to consider variation in acceleration)

HARD

Physics>Mechanics>Centre of Mass>Impulse

A solid ball of radius $0.2$$\mathrm{m}$ and mass $1$ $\mathrm{kg}$ lying at rest on a smooth horizontal surface is given an instantaneous impulse of $50$$\mathrm{N}\mathrm{s}$at point $\mathrm{P}$ as shown. The number of rotations made by the ball about its diameter before hitting the ground is

EASY

Physics>Mechanics>Centre of Mass>Impulse

A disc of mass $10\mathrm{g}$ is kept floating horizontally in the air by firing bullets, each of mass $5\mathrm{g}$, with the same velocity at the same rate of $10$ bullets per second. The bullets rebound with the same speed in positive direction. The velocity of each bullet at the time of impact is $(\text{Take}g=9.8\mathrm{m}{\mathrm{s}}^{-2})$