Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 1: Exercise-1

A rod $\left(AB\right)$ is attached to a fixed point $\left(C\right)$ using a light rope $\left(AC\right).$ The other end of the rod $\left(B\right)$ is sitting on ice with negligible friction and the system is in stationary position. Which of the following can be the equilibrium configuration of this system?

A person supports a book between finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of $W$ then the person is producing a torque on the book of

A string is wrapped around the rim of a wheel of moment of inertia $0.20 \mathrm{kg}-{\mathrm{m}}^2$ and radius $20\mathrm{cm}.$ The wheel is free to rotate about its axis and initially the wheel is rest. The string is now pulled by a force of $20 N.$ The angular velocity of the string after $5$ seconds will be :-

In the figure $\left(A\right)$ half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at $O.$ A force $F$ is applied at the end of steel part. In figure $\left(B\right)$ the steel part is pivoted at $\text{'}O\text{'}$ and the same force is applied at the wooden end:-

In the following figure $r_1$ and $r_2$ are $5\mathrm{cm}$ and $30\mathrm{cm}$ respectively. If the moment of inertia of the wheel is $5100 \mathrm{kg}-{\mathrm{m}}^2$ then its angular acceleration will be :-

A non uniform rod $OA$ of linear mass density $\lambda ={\lambda }_{0}x\left({\lambda }_0=\right.$ const.) is suspended from ceiling with hinge joint $O\mathit{ }\&$ light string as shown in figure. Find the angular acceleration of rod just after the string is cut

A particle of mass $m$ moves with a constant velocity. Which of the following statements is not correct about its angular momentum about $O :$

A thin rod of mass $M$ and length $L$ is struck at one end by a ball of clay of mass $m,$ moving with speed $v$ as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about $A,$ the midpoint of the rod, is