Figure shows a small bob of mass $m$ suspended from a point on a thin rod by a light inextensible string of length $l.$The rod is rigidly fixed on a circular platform. The platform is set into rotation. The minimum angular speed $\omega ,$ for which the bob loses contact with the vertical rod, is

The whole set up shown in the figure is rotating with constant angular velocity $\omega$ on a horizontal frictionless table. The ratio of tensions $\frac{T_1}{T_2}$ is ( Given, $\frac{I_2}{I_1}=\frac{2}{1}$ )

A body of mass $\text{'} m \text{'}$ is moving with constant speed $V$ on a track shown in figure. At point $A\&$ point $B$ radius of curvature is $R.N_A, N_B\&N_C$represents normal reactions at $A, B \& C,$ Which of the following option is correct ?

The acceleration of block $B$ is
(Assuming pulley and strings are light and frictionless)

A block of mass $m=2 \mathrm{kg}$ is suspended with a light spring of spring constant $k=1000 \mathrm{N} {\mathrm{m}}^{-1}.$ If the lift is moving vertically upward with acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$ then equilibrium elongation in the spring is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Two blocks $A$ and $B$ of mass $2m$ and $m$ respectively are connected to a spring of spring constant $k.$ A horizontal force $F=5mg$ is applied to block $A$ as indicated. If acceleration of block $B$ at the instant is $g,$ then acceleration of block $A$ at that instant is

A block of mass $4 \mathrm{kg}$ is placed on a rough fixed inclined plane as shown. The minimum force $F$ which is parallel to inclined to keep the block at rest is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

The magnitude of relative acceleration of $A$ w.r.t. $B$ is (Assuming pulley and string are light and massless)