A spherical uniform body of radius $R$, mass $M$ and moment of inertia $I$ rolls down (without slipping) on an inclined plane making an angle $\theta $ with the horizontal. Then its acceleration is
$\frac{{g\,\sin \,\theta }}{{1 - M{R^2}/I}}$
$\frac{{g\,\sin \,\theta }}{{1 + I/M{R^2}}}$
$\frac{{g\,\sin \,\theta }}{{1 + M{R^2}/I}}$
$\frac{{g\,\sin \,\theta }}{{1 - I/M{R^2}}}$
Two disc one of density $7.2\, g/cm^3$ and the other of density $8.9\, g/cm^3$ are of same mass and thickness. Their moments of inertia are in the ratio
A straight rod of length $L$ has one of its ends at the origin and the other at $x = L$. If the mass per unit length of the rod is given by $Ax$ (where $A$ is a constant), then where is its mass centre from origin ?
A man of $50\, kg$ mass is standing in a gravity free space at a heigth of $10\,m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed of $2\,m/s$. When the stone reaches the floor, the distance of the man above the floor will be ........ $m.$
$A$ non uniform rod $OA$ of linear mass density $\lambda = \lambda_0x$ $(\lambda_0 =$ const.) is suspended from ceiling with hinge joint $O$ & light string as shown in figure. Find the angular acceleration of rod just after the string is cut.
Find the torque of a force $\vec F = -3\hat i + \hat j + 5\hat k$ acting at the point $\vec r = 7\hat i + 3\hat j + \hat k$ with respect to origin