B M Sharma Solutions for Chapter: Rigid Body Dynamics: Part 1, Exercise 7: Exercises

$ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{\mathit{B}\mathit{C}}, I_{\mathit{C}\mathit{A}}$ are the moments of inertia of the plate about $AB, BC,CA$ respectively. Which one of the following relations is correct?

Two rings of same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is, (Mass of the ring$=m$, radius$=r$.)

Uniform rod $AB$ is hinged at end $A$ in horizontal position as shown in the figure. The other end is connected to a block through a massless string as shown. The pulley is smooth and massless. Masses of block and rod is same and is equal to $m$. Then acceleration of block just after release from this position is

A cubical block of side $L$ rests on a rough horizontal surface with coefficient of friction $\mu .$ A horizontal force $F$ is applied on the block as shown If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\mathrm{\theta }$ with $AB$ as shown in figure. The moment of inertia of the plate about the axis $CD$ is then equal to

Find minimum height of obstacle so that the sphere can stay in equilibrium

A sphere is placed rotating along its centre and initially at rest in a comer as shown in figure $\left(A\right) \text{\&} ( B)$. The coefficient of friction between all surfaces and the sphere is $\frac{1}{3}$. Find the ratio of the frictional force $\frac{f_A}{f_B}$ by ground in situations $\left(A\right) \text{\&} \left(B\right)$ is:

The moment of inertia of a thin square plate $ABCD$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is $I.$ Which of the following is false?