A forcetime Ft graph for a linear motion is shown in following figure The segments shown are circular The linear momentum gained between 0 and 8 seconds is (2024)

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

A carrom coin of radius $1.5\mathrm{cm}$and mass $5\mathrm{g}$strikes the side of the board at an angle $30°$with respect to the normal. The coin stays in contact with the side for ${10}^{-3}\mathrm{s}$and rebounds at an angle of $45°$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

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

The impulse is highest in figure.

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:

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

A ball of mass $3\mathrm{kg}$, moving with a speed of $100\mathrm{m}{\mathrm{s}}^{-1}$, strikes a wall at an angle $60°$ (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:

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 $\frac{\lambda }{4}$

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

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?

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 _____$\mathrm{N}\mathrm{s}$.

The correct dimensional formula for impulse is given by

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

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 :

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 :

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

The force $‘F\text{'}$ acting on a particle of mass $‘m\text{'}$ 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:

A $2000\mathrm{kg}$rocket in free space expels $0.5\mathrm{kg}$of gas per second at exhaust velocity $400\mathrm{m}{\mathrm{s}}^{–1}$ 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)

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

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 $(\text{Take}g=9.8\mathrm{m}{\mathrm{s}}^{-2})$