List of top Questions asked in MET

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to \(R^{-5/2}\), then \(T^2\) is proportional to :
A uniform thin bar of mass \(6m\) and length \(12L\) is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is:
A body is moving with constant velocity parallel to x-axis. Its angular momentum w.r.t. the origin will :
A solid sphere of radius R has moment of inertia \(I\) about its diameter. What will be moment of inertia of a shell of same mass and same radius about its diameter?
A particle of mass m is projected with a velocity v at an angle of \(45^\circ\) with horizontal. When the particle is at its maximum height, the magnitude of its angular momentum about the point of projection is:
A ball falls vertically on to a floor, with momentum \(p\), and then bounces repeatedly, the coefficient of restitution is \(e\). The total momentum imparted by the ball to the floor is:
A bullet is fired by a light rifle and the other with a heavy rifle by the same force. Which rifle will cause more injury to the shoulder?
A particle is moving in a circular path with a constant speed \(v\). If \(\theta\) is the angular displacement. Then starting from \(\theta = 0\), the maximum and minimum changes in the momentum will occur, when value of \(\theta\) is respectively:
The displacement x and time t for a particle are related to each other as \( t = \sqrt{x} + 3 \). What is work done in first 6 s of its motion?
An object A moving horizontally with kinetic energy of 800 J experiences a constant opposing force of 100 N, while moving from a place x to a place y, where xy is 2 m. What is the energy of A at y?
A force of 5 N gives a mass \(M_1\) an acceleration equal to \(8 \, \text{m/s}^2\) and \(M_2\) an acceleration equal to \(24 \, \text{m/s}^2\). What is the acceleration, if both masses are tied together?
A simple spring has length L and force constant k. It is cut into two springs of lengths \( l_1 \) and \( l_2 \) such that \( l_1 = n l_2 \) (n = an integer). The force constant of spring of length \( l_1 \) is:
A fireman weighing \(80\,\text{kg}\) slides down a pole. If the resisting force of friction is \(720\,\text{N}\), his acceleration would be: (take \( g = 10\,\text{m/s}^2 \))
A 4 kg block A is placed on the top of a block B of mass 8 kg, which rests on a smooth table. A just slips on B when a force of 12 N is applied on A. Then, the maximum horizontal force required to make both A and B move together is:
A particle p is moving in a circle of radius r with a uniform speed v, C is the centre of the circle and AB is the diameter. The angular velocity of p about A and C is in the ratio:
A particle is projected from the ground with an initial speed of u at an angle \( \theta \) with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is:
A particle of mass m is moving in a horizontal circle of radius R under the centripetal force \( = -\frac{k}{R^2} \) where k is a constant. What is the total energy of the particle?
A point initially at rest moves along x-axis. Its acceleration varies with time as \( a = (6t + 5)\, \text{m/s}^2 \). If it starts from origin, the distance covered in 2 s is:
A cyclist moving on a circular track of radius 40 m completes half a revolution in 40 s. Its average velocity is:
The displacement of an oscillating particle is given by \( y = A \sin[Bx + Ct + Dt] \). The dimensional formula for \( [ABCD] \) is:
The phrase ‘arrows of flying fire’
According to this passage, rockets were
The bombs have been referred to as “heaven shaking thunder” because they
According to this passage, rockets were invented by
Find the missing number in the triangle: