QUIZ 1:centre Of Mass,linear Momentum(#Free Test Series) - JEE MCQ

Two particles A and B start moving due to their mutual interaction only. If at any timet, a_A and a_B are their respective accelerations, v_A and v_B are their respective velocities, and up to that time W_A and W_B are the work done on A and B respectively by the mutual force, m_A and m_B are their masses respectively, then which of the following is always correct?

The centre of mass of a non-uniform rod of length L whose mass per unit length λ varies as λ=kx²/Lwhere k is a constant and x is the distance of any point on rod from its one end, is (from the same end)

In a system of particles 8 kg mass is subjected to a force of 16 N along +ve x−axis and another 8 kg mass is subjected to a force of 8 N along +ve y−axis. The magnitude of acceleration of centre of mass and the angle made by it with x−axis are given respectively by

In a gravity free space, a man of mass M standing at a height h above the floor, throws a ball of mass m straight down with a speed u. When the ball reaches the floor, the distance of the man above the floor will be

The velocities of two particles A and B of same mass are V_A=aî and V_B=bj^ where a and b are constants. The acceleration of particle A is (2ai^+4bj^) and acceleration of particle B is (ai^−4bj^) (in m/s²). The centre of mass of two particle will move in

A bar of mass ′m′ length ℓ is pure translator motion with its centre velocity v. It collides with another identical bar which is in rest and sticks to it. Assume that after the collision it becomes one system, then the angular velocity of the system after the collision is

An object of mass 3m splits into three equal fragments. Two fragments have velocities vj^ and vi^. The velocity of the third fragment is

Distance of the centre of mass of a solid uniform cone from its vertex is z₀. If the radius of its base is R and its height is h then z₀ is equal to

Two objects that are moving along an xy-plane on a frictionless floor collide. Assume that they form a closed, isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision. Before collision After collision   

A ball is projected in a direction inclined to the vertical and bounces on a smooth horizontal plane. The range of one rebound is R. If the coefficient of restitution is e, then range of the next rebound is

Three blocks are initially placed as shown in the figure. Block A has mass m and initial velocity v to the right. Block B with mass and block C with mass 4m are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of blocks A is  

A block of mass m starts from rest and slides down a frictionless semi-circular track from a height h as shown. When it reaches the lowest point of the track, it collides with a stationary piece of putty. also having mass m. If the block and the putty stick together and continue to slide, the maximum height that the block-putty system could reach is