Maharashtra Board Solutions for Chapter: Laws of Motion, Exercise 3: Exercises

The rough surface of a horizontal table offers a definite maximum opposing force to initiate the motion of a block along the table, which is proportional to the resultant normal force given by the table. Forces $\mathrm{F}1$ and $\mathrm{F}2$ act at the same angle $\mathrm{\theta }$ with the horizontal and both are just initiating the sliding motion of the block along the table. Force $\mathrm{F}1$ is a pulling force while the force $\mathrm{F}2$ is a pushing force. $\mathrm{F}2 > \mathrm{F} 1$ , because

Discuss the following a special case of elastic collision: A very light object collides on a comparatively much massive object initially at rest. Calculate the ratio of final speed of lighter object to the initial speed of the lighter object.

Ten identical masses (m each) are connected one below the other with $10$ strings. Holding the topmost string, the system is accelerated upwards with acceleration $\mathrm{g}/2$. What is the tension in the $6\mathrm{th}$ string from the top (Topmost string being the first string)?

A ball of mass $100 \mathrm{g}$ dropped on the ground from $5 \mathrm{m}$ bounces repeatedly. During every bounce $64\%$of the potential energy is converted into kinetic energy. Calculate the Coefficient of restitution.

A ball of mass $100 \mathrm{g}$ dropped on the ground from $5 \mathrm{m}$ bounces repeatedly. During every bounce $64\%$ of the potential energy is converted into kinetic energy. Calculate the following: 

(b) Speed with which the ball comes up from the ground after third bounce.

A ball of mass $100 \mathrm{g}$ dropped on the ground from$5 \mathrm{m}$ bounces repeatedly. During every bounce $64\%$ of the potential energy is converted into kinetic energy. Calculate the impulse(magnitude) given by the ball to the ground during this bounce in $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$.

A ball of mass $100 \mathrm{g}$ undefined dropped on the ground from $5 \mathrm{m}$ undefined bounces repeatedly. During every bounce $64\%$ undefined of the potential energy is converted into kinetic energy. Calculate the following:

(d) Average force exerted by the ground if this impact lasts for $250 \mathrm{ms}.$

A ball of mass $100 \mathrm{g}$ dropped on the ground from $5 \mathrm{m}$ bounces repeatedly. During every bounce $64\%$ of the potential energy is converted into kinetic energy. The average pressure exerted by the ball on the ground during this impact if contact area of the ball is $0.5 {\mathrm{cm}}^2$ is $9.12\times {10}^k \mathrm{N}/{\mathrm{m}}^2$. What is the value of $k$?