Embibe Experts Solutions for Chapter: Laws of Motion, Exercise 3: Level 3

A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F\left(t\right)=F_0{e}^{–\mathrm{bt}}$ in the $x$-direction. Its speed $v\left(t\right)$ is depicted by which of the following curves?

Newton's Third law is equivalent to the 

A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same kinetic energy $E_0$. The minimum energy of explosion will be

Hammer of mass $M$ strikes a nail of mass $m$ with a velocity $20 \mathrm{m} {\mathrm{s}}^{-1}$ into a fixed wall. The nail penetrates into the wall to a depth of $1 \mathrm{cm}.$ The average resistance of the wall to the penetration of the nail is,

A hemisphere of mass $3 \mathrm{m}$ and radius $R$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. If the particle is displaced with a negligible velocity, then find the angular velocity of the particle relative to the centre of the hemisphere at an angular displacement $\mathrm{\theta },$ when the velocity of the hemisphere is $v$.

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 newton and $t$ in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

A block of mass $m$ is held fixed against a wall by applying a horizontal force $F$. Which one of the following options is incorrect.

A bus is moving in a circular horizontal track of radius $10 \mathrm{m}$ with a constant speed $10 \mathrm{m} {\mathrm{s}}^{-1}$. A plumb bob is suspended from the roof of the bus by a light rigid rod of length $1.0 \mathrm{m}$. The angle made by the rod with the track is (take $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$