Embibe Experts Solutions for Chapter: Laws of Motion, Exercise 1: JEE Main - 19th April 2014

The figure represents the momentum time $(p-t)$ curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ?

If $\left(t_3-t_2\right)<t_1$

A block of $\sqrt{3} \mathrm{kg}$ is attached to a string whose other end is attached to the wall. An unknown force $F$ is applied so that the string makes an angle of $30°$ with the wall. The tension $T$ is : (Given g $=10 \mathrm{m} {\mathrm{s}}^{–2}$)

A machine gun of mass $10 \mathrm{kg}$ fires $20 \mathrm{g}$ bullets at the rate of $180$ bullets per minute with a speed of $100 \mathrm{m} {\mathrm{s}}^{–1}$ each. The recoil velocity of the gun is :

$100$ balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $t \mathrm{s}$. The total force exerted by the balls on the wall is

A body of mass $10 \mathrm{kg}$ is moving with an initial speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. The body stops after $5 \mathrm{s}$ due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A block of mass $5 \mathrm{kg}$ is placed at rest on a table of rough surface. Now, if a force of $30 \mathrm{N}$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50 \mathrm{m}$ in an interval of time $10 \mathrm{s}$. Coefficient of kinetic friction is (given, $g = 10 \mathrm{m} {\mathrm{s}}^{–2}$ ):

As shown in the figure a block of mass $10 \mathrm{kg}$ lying on a horizontal surface is pulled by a force F acting at an angle $30°$, with horizontal. For ${\mu }_s=0.25$, the block will just start to move for the value of $F$: [Given g $= 10 \mathrm{m}·{\mathrm{s}}^{–2}$]

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

The impulse is highest in figure.