Anil Ahlawat Solutions for Chapter: Gravitation, Exercise 1: EXERCISES

A coil of wire with cross-sectional area $0.5 {\mathrm{mm}}^2$ weighs $75 \mathrm{g}$ in air and $65 \mathrm{g}$ in water. The length of the coil in $\mathrm{cm}$ is

A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of ball above the ground in $\frac{T}{5}$ seconds?

The gravitational force between two masses kept at a certain distance is $p N$. The same two masses are now kept in water and the distance between them are same. The gravitational force between these two masses in water is $q N$. Then

Consider the following figures $1$ and $2$. In figure $1$, the mass of the body $A$ in air is $0.2 \mathrm{kg}$. The mass of the water container (with water in it) is $0.5 \mathrm{kg}$. In figure $2$, when $A$ is completely immersed in the water of the container $B$, the readings of the respective balances change as shown.

What is the value of $X$?

Suppose, the acceleration due to gravity at the Earth's surface is $10 {\mathrm{ms}}^{-2}$ and at the surface of Mars is $4 {\mathrm{ms}}^{-2}$. A $60 \mathrm{kg}$ passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the figure best represents the weight (net gravitational force) of the passenger as a function of time?

A tank $2 \mathrm{m}$ high is half filled with water and then filled to the top with oil of density $0.60 \mathrm{g}/\mathrm{cc}$. What is the pressure at the bottom of the tank due to these liquids? (Take $g=10 {\mathrm{ms}}^{-2}$)

An object floats in water such that $\frac{1}{4}$the of its volume is above the surface of water. When the same object is made to float in sample of impure alcohol, the volume that remains outside the liquid is $\frac{1}{10}$ of total volume. The relative density of the sample of alcohol will be

Two fixed point masses of $10 \mathrm{kg}$ and $20 \mathrm{kg}$ are located at $\left(0 \mathrm{m}, 0 \mathrm{m}\right)$ and $\left(5 \mathrm{m}, 0 \mathrm{m}\right)$. Where should a third point mass of $30 \mathrm{kg}$ be kept so that the net force of attraction on $30 \mathrm{kg}$ mass due to point masses $10 \mathrm{kg}$ and $20 \mathrm{kg}$ is zero?