$A$ particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u^2}{25 g}$,where the value of $n$ is (Given $g$ is the acceleration due to gravity).

$A$ ball of mass $160 \, g$ is thrown up at an angle of $60^{\circ}$ to the horizontal at a speed of $10 \, m/s$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly $\left(g=10 \, m/s^{2}\right)$ (in $kg \cdot m^{2}/s$).

$A$ mass of $2 \, kg$ is whirled in a horizontal circle by means of a string at an initial speed of $5$ revolutions per minute. Keeping the radius constant,the tension in the string is doubled. The new speed is nearly ....... $rpm$.

$A$ person walks in such a way that he covers equal distance in each step. The person takes $2$ steps forward towards East, then takes a right turn and walks $4$ steps towards South, then takes a right turn and walks $6$ steps towards West, and then takes a right turn and walks further. The direction of his final position after a total of $20$ steps walk with respect to his initial position is:

Four persons $P, Q, R$ and $S$ are initially at the four corners of a square of side $d$. Each person now moves with a constant speed $v$ in such a way that $P$ always moves directly towards $Q$,$Q$ towards $R$,$R$ towards $S$,and $S$ towards $P$. The four persons will meet after time:

$A$ car goes around a uniform circular track of radius $R$ at a uniform speed $v$ once in every $T$ seconds. The magnitude of the centripetal acceleration is $a_c$. If the car now goes uniformly around a larger circular track of radius $2R$ and experiences a centripetal acceleration of magnitude $8a_c$,then its time period is: