A stone is projected from a horizontal plane. It attains maximum height \(H,\) and strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assuming the collision to be elastic, the height of the point on the wall where the ball will strike will be:

           

1.	\(\dfrac{H}{2} \)	2.	\(\dfrac{H}{4} \)
3.	\(\dfrac{3 H}{4} \)	4.	None of these

Potential energy \((U)\) related to coordinates is given by; \(U=3(x+y).\) Work done by the conservative force when the particle is going from \((0,0), (2,3)\) is:
1. \(15\) J
2. \(-15\) J
3. \(12\) J
4. \(10\) J

A position dependent force \(F=7-2x+3x^2\) N acts on a small body of mass \(2\) kg and displaces it from \(x = 0\) to \(x = 5\) m. The work done in joule is:

Three different objects of mass $m_1,$ $m_2$ and m₃ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of:

A body is thrown vertically up with a certain initial velocity. The potential and the kinetic energy of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of the potential and the kinetic energies of the body when it crosses at the same point will be: 

1. 1:1

2. 1:4

3. 1:7

4. 1:8

A man pushes a wall and fails to displace it. He does:
1. negative work
2. positive but not maximum work
3. no work at all
4. maximum work

The minimum work done in pulling up a block of wood weighing \(2\) kN for a length of \(10\) m on a smooth plane inclined at an angle of \(15^\circ\) with the horizontal is (given: \(\mathrm{sin}15^\circ=0.2588)\):
1. \(4.36\) kJ
2. \(5.17\) kJ
3. \(8.91\) kJ
4. \(9.82\) kJ

A spherical ball of mass \(20\) kg is stationary at the top of a hill of height\(100\) m. It slides down a smooth surface to the ground, then climbs up another hill of height \(30\) m and finally slides down to a horizontal base at a height of \(20\) m above the ground. The velocity attained by the ball is: 
1. \(10 \) m/s
2. \(10 \sqrt{30} \) m/s
3. \(40 \) m/s
4. \(20 \) m/s