Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Force, Exercise 2: Critical Thinking

In a gravitational force field a particle is taken from $A$   to $B$ along different paths as shown in figure. Then

A shell is fired from a cannon with a velocity $v$ $\left(\mathrm{m} {\mathrm{s}}^{-1}\right)$  at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon with speed $v \cos \theta$ then the speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) of the other piece immediately after the explosion is

A machine gun has a mass $5 \mathrm{kg}$. It fires $50$ gram bullets at the rate of $30$ bullets per minute at a speed of $400 \mathrm{m} {\mathrm{s}}^{-1}.$ What force is required to keep the gun in position?

A rocket of initial mass $6000 \mathrm{kg}$ ejects gases at a constant rate of $16 \mathrm{kg} {\mathrm{s}}^{-1}$ with constant relative speed of $11 \mathrm{km} {\mathrm{s}}^{-1}$. What is the acceleration of rocket one minute after the blast?

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

A solid sphere of mass $2 \mathrm{kg}$   is resting inside a cube as shown in the figure. The cube is moving with a velocity  $\overrightarrow{v}=(5\mathrm{t}\hat{\mathrm{i}}+2\mathrm{t}\hat{\mathrm{j}})\mathrm{m} {\mathrm{s}}^{-1}$
Where t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube? (Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$  )

Consider the following statement: When jumping from some height, you should bend your knees as you come to rest, instead, of keeping your legs stiff. Which of the following relations can be useful in explaining the statement?

Which of the following has maximum momentum?