Two stones are thrown with the same speed $u$ at different angles from the ground into the air. If both stones have the same range and the heights attained by them are $h_1$ and $h_2$,then $h_1 + h_2$ is equal to .......

$A$ body is projected from the earth at an angle of $30^{\circ}$ with the horizontal with some initial velocity. If its range is $20 \ m$,the maximum height reached by it is: (in meters)

According to the quantum theory,a photon of electromagnetic radiation of frequency $v$ has energy $E = h v$,where $h$ is known as Planck's constant. According to the theory of relativity,a particle of mass $m$ has equivalent energy $E = m c^2$,where $c$ is the speed of light. Thus,a photon can be treated as a particle having effective mass $m = \frac{h v}{c^2}$. If a flash of light is sent horizontally in the Earth's gravitational field,then photons while travelling a horizontal distance $d$ would fall through a vertical distance given by:

Two paper screens $A$ and $B$ are separated by a distance of $100\,m$. $A$ bullet pierces $A$ and then $B$. The hole in $B$ is $10\,cm$ below the hole in $A$. If the bullet is travelling horizontally at the time of hitting $A$,then the velocity of the bullet at $A$ is $.......\,m/s$.

$A$ bob of mass $0.1\; kg$ hung from the ceiling of a room by a string $2\; m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a)$ at one of its extreme positions,
$(b)$ at its mean position.

$A$ ball is thrown upwards and it returns to the ground describing a parabolic path. Which of the following remains constant?