List of top Physics Questions on Rotational Motion and Torque

An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______

A solid cylinder having radius \(R\) and length \(L\) is slipping on a rough horizontal plane. At time \(t = 0\) the cylinder has a translational velocity \(v_0 = 49\) m/s, perpendicular to its axis and a rotational velocity \(v_0/4R\) about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction \(\mu_k = 0.25\) and \(g = 9.8\) m/s²)
The position of an object having mass \(0.1\) kg as a function of time \(t\) is given as} \[ \vec r = (10t^2\hat{i}+5t^3\hat{j})\ \text{m}. \] At \(t=1\) s, which of the following statements are correct?} A.} Linear momentum \( \vec p = (2\hat{i}+1.5\hat{j})\) kg m/s. B.} Force acting on the object \( \vec F = (2\hat{i}+3\hat{j})\) N. C.} Angular momentum about origin \( \vec L = 15\hat{k}\) J s. D.} Torque about origin \( \vec \tau = 20\hat{k}\) N m. Choose the correct answer.

A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _______ (g = acceleration due to gravity).

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is \(\frac{x}{12} ML^2\) kg m\(^2\). The value of x is ______ .

A capacitor of capacitance 10 μF is connected with a battery of emf 6V. Now the battery is disconnected and another uncharged capacitor of capacitance 20 μF is connected to the capacitor. Find the charge on the 20 μF capacitor.
A circular disk of radius \( R \) meter and mass \( M \) kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that \( \theta(t) = 5t^2 - 8t \), where \( \theta(t) \) is the angular position of the rotating disk as a function of time \( t \). How much power is delivered by the applied torque, when \( t = 2 \) s?
A disc is performing pure rolling if the speed of the top point is 8 m/s. Find the speed of point B.
A solid sphere of mass \( m \) and radius \( r \) is allowed to roll without slipping from the highest point of an inclined plane of length \( L \) and makes an angle of \( 30^\circ \) with the horizontal. The speed of the particle at the bottom of the plane is \( v_1 \). If the angle of inclination is increased to \( 45^\circ \) while keeping \( L \) constant, the new speed of the sphere at the bottom of the plane is \( v_2 \). The ratio of \( v_1^2 : v_2^2 \) is: