Instantaneous Force and Impulse

Q.

A cricket ball of mass 150 gm is moving with a velocity of 12 m/s and is hit by a bat so that the ball is turned back with a velocity of 20 m/s. The force of blow acts for 0.01s on the ball. The average force exerted by the bat on the ball is

1. 600 N

2. 500 N

3. 400 N

4. 480 N

Q. If velocity $\left[\text{V}\right]$ time $\left[\text{T}\right]$ and force $\left[\text{F}\right]$ are chosen as the base quantities, the dimensions of the mass will be

1. $\left[\text{F}\text{V}{\text{T}}^{-1}\right]$
2. $\left[\text{F}{\text{T}}^2\text{V}\right]$
3. $\left[\text{F}{\text{T}}^{-1}{\text{V}}^{-1}\right]$
4. $\left[\text{F}\text{T}{\text{V}}^{-1}\right]$

Q. A metal plate of mass $200gm$ is balanced in mid–air by throwing $40$ balls/sec, each of mass $2gm$, vertically upwards from below. The balls rebound with the same speed with which they strike the plate. Find the velocity with which the balls strike the plate. (Take $g=10m/s^2$)

1. $20m/s$
2. $10m/s$
3. $5m/s$
4. $12.5m/s$

Q.

A ball of mass 1 kg is dropped from 20 m height on ground and it rebounds to height 5m. Find magnitude of change in momentum during its collision with the ground.[ Take g =10m/s^{​​​​​2​​}

Q.

If a body of mass M collides against a wall with velocity V and rebounds with the same velocity, its change of momentum is:

1. Zero

2. $Mv$

3. $-Mv$

4. $-2Mv$

Q. The figure shows the position-time (x-t) graph of one-dimensional motion of a particle of mass 0.4 kg. Find the magnitude of impulse imparted to the particle at $t=2\text{s}\text{and}4\text{s}$ respectively.

1. $0.2\text{Ns}$ and $0.4\text{Ns}$
2. $0.4\text{Ns}$ and $0.4\text{Ns}$
3. $0.8\text{Ns}$ and $0.4\text{Ns}$
4. $0.8\text{Ns}$ and $0.8\text{Ns}$

Q. A particle of mass $M$ orginally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F=F_0[1-{\left(\frac{t-T}{T}\right)}^2]$
where $F_0$ and $T$ are constants. The force acts only for the time interval $2T$. The velocity $v$ of the particle after time $2T$ is :

1. $\frac{2F_{0}T}{M}$
2. $\frac{F_{0}T}{2M}$
3. $\frac{4F_{0}T}{3M}$
4. $\frac{F_{0}T}{3M}$

Q.

How do you use impulse-momentum theorem?

Q.

A stream of water flowing horizontally with a speed of $15m{s}^{-1}$ gushes out of a tube of cross-sectional area ${10}^{-2}{m}^2$, and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound?

Q.

A rocket with a lift-off mass 20, 000 kg is blasted upwards with an initial acceleration of $5.0m{s}^{-2}$. Calculate the initial thrust (force) of the blast.

Q.

Is the impulse-momentum relationship related to Newtons second law

Q. Two short electric dipoles at a certain distanceapply a force F on each other. If the separation is doubled, then the force of interaction between the dipoles, will become approximately

Q. A ball of mass $50\text{g}$ and relative density $0.5$ strikes the surface of water with a velocity of $20\text{m/s}$. It comes to rest at a depth of $2\text{m}$. Find the work done by the resisting force in water.
$($Take, $g=10{\text{m/s}}^2)$

1. $-6\text{J}$
2. $-7\text{J}$
3. $-9\text{J}$
4. $-8\text{J}$

Q.

If a constant force acts on a body initially kept at rest the distance moved by the body in time T is proportional to

(A) t (B) t² (C) t³

Please explain why t² i answer.

Q. A disc of mass $100g$ is kept floating horizontally in the air by firing bullets each of mass $5g$ with the same velocity at the same rate of $10$ bullets per second. The bullets rebound at the same speed in opposite direction. Then, the velocity of each bullet at the time of impact is: (Take $g=10m/s^2)$

1. $1000m/s$
2. $100m/s$
3. $50m/s$
4. $10m/s$

Q. A bullet is fired from a gun. The force on the bullet is given by $F=600-2\times {10}^{5}t$, where $F$ is in newtons and $t$ in seconds. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet.

1. Zero
2. $9\text{Ns}$
3. $0.9\text{Ns}$
4. $1.8\text{Ns}$

Q.

A ball of mass 0.2 kg rests on a vertical post of height 5m. A bullet of mass 0.01 kg travelling with a velocity v m/s in a horizontal direction, hits the centre of the ball. After the collision the ball and bullet travel independently. The ball hits the ground at a distance of 20m and the bullet at a distance of 100m from the foot of the post. The initial velocity of the bullet is

And is 500m/s.

Please give detailed explanation as I won't be able to understand concise answers.

Q.

Define the terms momentum and impulse. Obtain the relation between impulse and momentum.

Q. A 150 kg merry go round in the shape of a uniform solid horizontal disc of radius 2 m is set in motion by wrapping a rope around the rim of disc and pulling on the rope. What constant force must be exerted on the rope to bring the merry go round from rest to an angular speed of $0.5$ rev/s in 2 s ?

1. 574 N
2. 314 N
3. 81 N
4. 157 N

Q. A gun fires $10$ bullets/sec each of mass $10\text{gm}$, with a muzzle velocity of $50\text{m/s}$. Find the force required to hold the gun in position.

1. $5\text{N}$
2. $10\text{N}$
3. $15\text{N}$
4. $20\text{N}$

Q. what is sticky ends?

Q.

Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for $t<0,t>4s,0<t<4s$?
(b) impulse at t = 0 and t = 4 s?
(Consider one-dimensional motion only).

Q. A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along x-axis. Its kinetic energy $K$ changes with time as $\frac{dK}{dt}=rt$ where $r$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

1. The force applied on the particle is constant.
2. The speed of the particle is proportional to time.
3. The distance of the particle from the origin increases linearly with time.
4. The force is conservative.

Q. The magnitude of the force (in $N$) acting on a body varies with time $t$ (in $\mu s$) as shown. $AB,BC$ and $CD$ are straight line segments. The magnitude of the total impule of the force on the body from $t=4\mu s$ to $t=16\mu s$ is

1. $5\times {10}^{-3}\text{Ns}$
2. $5.8\times {10}^3\text{Ns}$
3. $5.8\times {10}^{-3}\text{Ns}$
4. $5\times {10}^3\text{Ns}$

Q.

A force of 50 dynes is acted on a body of mass 5 g which is at rest for an interval of 3 seconds, then impulse is

1. 

2. 

3. 

4. 

Q. A disc of mass 10grams is kept floating horizontally by throwing 10 marbles per second against it from below . The marbles strike normally and rebound down with same speed . If mass of each marble is 5 grams the the velocity at which they are striking the disc

Q.

If the error in the measurement of momentum of a particle is 50% , then the error in the measurement of kinetic energy is how much?

a)75% b)125%

Q. A thin uniform rod of mass $m$ and length $l$ is kept on a smooth horizontal surface such that it can move freely. At what distance $x$ from the centre of the rod should a particle of mass $m$ strike on the rod such that the point $P$ at a distance $\frac{l}{3}$ from the end of the rod is instantaneously at rest just after the elastic collision ?

1. $\frac{l}{3}$
2. $\frac{l}{6}$
3. $\frac{l}{4}$
4. $\frac{l}{2}$

Q. Acceleration of $10\text{kg}$ block is given as $a=(20-2t){\text{m/s}}^2$, where $t$ is in $\text{seconds}$. Find the average impulse imparted to the block during the time interval $0$ to $5$ $\text{sec}$.

1. $500\text{N.s}$
2. $1000\text{N.s}$
3. $250\text{N.s}$
4. $750\text{N.s}$

Q. A particle of mass $10\text{kg}$ is moving in a straight line. If its position $x$ with time $t$ is given by $x\left(t\right)=(t^3-2t-10)$ $\text{m}$, then the force acting on it at the end of $4^{th}$ second is

1. $24\text{N}$
2. $240\text{N}$
3. $300\text{N}$
4. $1200\text{N}$