Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Force, Exercise 3: Competitive Thinking

Assertion: A table cloth can be pulled from a table without dislodging the dishes.

Reason: To every action, there is an equal and opposite reaction.

A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\mathrm{\theta }$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\mathrm{\theta }$ for the block to remain stationary on the wedge is, 

Two blocks of equal mass are released on two smooth sides of a double inclined plane with a fixed base as shown in the figure. If each angle of inclination is $45°,$ the acceleration of the centre of mass of the system of the two blocks is $($acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}),$

A body of mass $\left(4 \mathrm{m}\right)$ is lying in $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces each of mass $\left(m\right)$ move perpendicular to each other with equal speeds $\left(v\right)$. The total kinetic energy generated due to explosion is,

A particle of mass $m$ is driven by a machine that delivers $k$ a constant power watts. If the particle starts from rest the force on the particle at time $t$ is 

The mass of a hydrogen molecule is $3.32\times {10}^{-27} \mathrm{kg}.$ If ${10}^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2 {\mathrm{cm}}^2$ at an angle of $45°$ to the normal and rebound elastically with a speed of ${10}^3 \mathrm{m} {\mathrm{s}}^{-1},$ then the pressure on the wall is nearly:

A lift weighing $250 \mathrm{kg}$ is to be lifted up at a constant velocity of $0.20 \mathrm{m}$ . What would be the minimum horse power of the motor to be used? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $P_{\mathrm{d}}$; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $P_{\mathrm{c}}.$ The values of $P_{\mathrm{d}}$ and $P_{\mathrm{c}}$ are respectively: