$A$ ball of mass $m$ is thrown vertically upwards. Another ball of mass $2m$ is thrown at an angle $\theta$ with the vertical. Both of them stay in air for the same period of time. The heights attained by the two balls are in the ratio of

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta_1$ and $\theta_2$ respectively from the horizontal,then answer the following question. If $v_1 \cos \theta_1 = v_2 \cos \theta_2$,then choose the incorrect statement.

$A$ body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same,then which of the following statements is true?

$A$ smooth circular groove has a smooth vertical wall as shown in the figure. $A$ block of mass $m$ moves against the wall with a speed $v$. Which of the following curves represents the correct relation between the normal reaction $(N)$ on the block by the wall and the speed of the block $(v)$?

$A$ body of mass $1\,kg$ is projected with velocity $50\,m/s$ at an angle of $30^{\circ}$ with the horizontal. At the highest point of its path,a force of $10\,N$ starts acting on the body for $5\,s$ vertically upward in addition to the gravitational force. What is the horizontal range of the body? $\left(g=10\,m/s^2\right)$

$A$ boy ties a stone of mass $100 \,g$ to the end of a $2 \,m$ long string and whirls it around in a horizontal plane. The string can withstand a maximum tension of $80 \,N$. If the maximum speed with which the stone can revolve is $\frac{K}{\pi} \,rev/min$,find the value of $K$. (Assume the string is massless and unstretchable)