Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $\vec P$ of magnitude 100N is applied at point A of the frame. Suppose the force $\vec P$ is resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN. The value of x, to the nearest integer, is————.
Let $f:R \to R$ be a continuous function such that $f(x) + f(x + 1) = 2$, for all $x\in R$. If ${I_1} = \int\limits_0^8 {f(x)dx} $ and ${I_2} = \int\limits_{ – 1}^3 {f(x)dx} $, then the value of $I_1 +2I_2 $ is equal to …… Continue reading $f(x) + f(x + 1) = 2$
Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its centre and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure. Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad/s. The value of n, to the nearest integer, is ———. [Given : In one complete revolution, the disk rotates by 6.28 rad] Continue reading Consider a 20 kg uniform circular disk …→
A horizontal force F is applied at the center of mass of a cylindrical object of mass m and radius R, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is μ. The center of mass of the object has an acceleration a. The acceleration due to gravity is g. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?
(A) For the same F, the value of a does not depend on whether the cylinder is solid or hollow
(B) For a solid cylinder, the maximum possible value of a is 2μg
(C) The magnitude of the frictional force on the object due to the ground is always μmg
(D) For a thin-walled hollow cylinder, $𝑎 = \frac {𝐹}{2𝑚}$ Continue reading A horizontal force F is applied at the center of mass …→
