Two insects P and Q are firmly sitting at the ends of a massless semicircular wire of radius R and two more insects A and B are firmly sitting at the bottom of the wire. The wire is given an angular velocity w0 about a vertical axis through its centre as shown in the figure. Mass of each insect is M. Now A and B crawl to the opposite ends to meet P and Q. Final angular velocity attained by the rod is equal to

A rectangular plate of mass 20kg is suspended from points A and B as shown. If pin B is removed determine the initial angular acceleration (in

An L shaped thin uniform rod of total length 2l is free to rotate in a vertical plane about a horizontal axis at P as shown in the figure The bar is released from rest. Neglect air and contact friction. The angular velocity at the instant it has rotated through 90° and reached the dotted position shown is

Two solid uniform disks of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks are A force F is applied to each disk at its edge for the same amount of time. Assume that friction at pulley axis is negligible. What statement is true about the kinetic energy (K) and magnitude of angular momentum (L) of the disks?

A thin plate of mass M, length L, and width 2d is mounted vertically on a frictionless axle along the z-axis, as shown. Initially the object is at rest. It is then tapped with a hammer to provide a torque , which produces an angular impulse H about the z-axis of magnitude What is the angular speed w of the plate about the z-axis after the tap?

Three equal masses m are rigidly connected to each other by massless rods of length l forming an equilateral triangle, as shown above. The assembly is to be given an angular velocity about an axis perpendicular to the triangle. For fixed , the ratio of the kinetic energy of the assembly for an axis through B compared with that for an axis through A is equal to

A uniform rectangular solid of side length L and width w placed on a frictionless incline of variable angle, . Assume that there is a very tiny peg preventing the box from sliding down the incline at the point labeled P. At what angle of incline will the box begin to tip over?

Two particles A and B of mass 5 kg and 9 kg respectively rest on the smooth faces of a fixed wedge as shown in the figure. They are connected by a light inextensible string passing over a smooth pulley at C and are released from rest from the position shown in the diagram. In the subsequent motion B hits the ground and does not rebound. Find

A chain of length L weighing l per unit length begins to fall through a hole in the ceiling.

The velocity of the cart at time t

A rod of length 1000 mm and coefficient of linear expansion a = 10–4 per degree is placed symmetrically between fixed walls separated by 1001 mm. The Young’s modulus of the rod is 1011 N/m2 . If the temperature is increased by 20°C, then the stress developed in the rod is

If coefficient of friction between the two blocks is equal to 0.4, then magnitude of initial slope (in S.I. unit) versus t (in SI unit) will be:

If the angles of a triangle are in ratio 4 : 1 : 1 then the ratio of the longest side and perimeter of triangle is -

So, the ratio of the longest side and perimeter of triangle is

In a triangle PQR as shown in figure given that x : y : z :: 2 : 3 : 6, then the value of QPR is -

If the sides be a, b, c then (r + r₁) tan+ (r + r₂) tan+ (r + r₃) tan =

If in a triangle ABC; AD, BE and CF are the altitudes and R is the circum-radius, then the radius of the circle DEF is -

Therefore, the radius of the circle DEF is R/2.