Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end A of the handle will be _________ \(Mr^2\).
The magnitude of vectors \(\vec{OA}\), \(\vec{OB}\) and \(\vec{OC}\) in the given figure are equal. The direction of \(\vec{OA} + \vec{OB} - \vec{OC}\) with x-axis will be :
Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \( \frac{24}{\pi} \times 10^2 \) Nm\(^{-2}\). What is the minimum radius of the wire ? (take g=10 ms\(^{-2}\))
The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m\(^2\).
The angle between vector \( (\vec{A}) \) and \( (\vec{A} - \vec{B}) \) is:
Match List - I with List - II : Choose the most appropriate answer from the options given below :