BM Sharma Solutions for Chapter: Newton's Laws of Motion I, Exercise 1: DPP

A mass of $1\mathrm{ }\mathrm{kg}$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If the string $C$ is stretched slowly, then

A machine gun is mounted on a $2000 \mathrm{kg}$ car on a horizontal frictionless surface. At some instant, the gun fires bullets of mass $10 \mathrm{g}$ with a velocity of $500\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ with respect to the car. The number of bullets fired per second is $10$. The average thrust on the system is

A machine gun fires a bullet of mass $40 \mathrm{gm}$ with a velocity of $1200 \mathrm{m} {\mathrm{s}}^{-1}$. The man holding it can exert a maximum force of $144\mathrm{ }\mathrm{N}$ on the gun. How many bullets can he fire per second at the most?

In the figure below, given is the position-time graph of a particle of mass $0.1 \mathrm{kg}$. The impulse at $t=2 \sec$ is

A body of mass $2$ $\mathrm{kg}$ has an initial velocity of $3 \mathrm{m} {\mathrm{s}}^{-1}$ along $OE$, and it is subjected to a constant force of $4\mathrm{ }\mathrm{N}$ in a direction perpendicular to $OE$. The distance of the body from $O$ after $4 \mathrm{seconds}$ will be

A particle moves in the $xy$ plane under the action of a force $\overrightarrow{F}$, such that the components of its linear momentum $\overrightarrow{p}$ at any time $t$ are $p_{\mathrm{x}}=2\cos t$ and $p_{\mathrm{y}}=2\sin t$. The angle between $\overrightarrow{F}$ and $\overrightarrow{p}$ at a time $t$ is

The motion of a particle of mass $m$ is given by $x=0$ for $t=0 \mathrm{s}$, $x\left(t\right)=A\sin \left(4\mathrm{\pi }t\right)$ for $0<t<\left(\frac{1}{4}\right) \mathrm{s}$ and $x=0$ for $t>\left(\frac{1}{4}\right) \mathrm{s}$ $\left(A>0\right)$. Which of the following statements are true?

Two billiard balls $A$ and $B$, each of mass $50 \mathrm{gm}$ are moving in the opposite directions with a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$. Each ball collides and rebounds at the same speed. If the collision lasts for ${10}^{-3} \sec$, which of the following statements are true?