A bomb of mass $1 \,kg$ initially at rest, explodes and breaks into three fragments of masses in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed $15 \,m / s$ each. The speed of heavier fragment is ……….. $m / s$

A light string passing over a smooth light pulley connects two block of masses $m_1$ and  $m_2$ (vertically). If the acceleration of the system is $\left( {\frac{g}{8}} \right)$, then the ratio of masses is

In the figure the tension in the diagonal string is $60\,N$.

Find the magnitude of the horizontal force $\overline{ F }_1$ and $\overline{ F }_2$ that must be applied to hold the system in the position shown.

A rocket with a lift-off mass $2\times10^4\, kg$ is blasted upwards with an intial acceleration of $5\, m\, s^{-2}$. The initial thrust of the blast is (Take $g = 10\, m\, s^{-2}$)

For the equilibrium of a body on an inclined plane of inclination $45^{\circ}$. The coefficient of static friction will be