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:

1.	\(70\)	2.	\(270\)
3.	\(35\)	4.	\(135\)

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:

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. \(15~\text J\)
2. \(-15\text{ J}\)
3. \(12\text{ J}\)
4. \(10\text{ J}\)

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

A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If \(g\) is the acceleration due to gravity, the work required to pull the hanging part on the table is:
1. \(MgL\)

2. \(\dfrac{MgL}{3}\)

3. \(\dfrac{MgL}{9}\)

4. \(\dfrac{MgL}{18}\)

A particle of mass 'm' is moving in a horizontal circle of radius 'r' under a centripetal force equal to –K/r², where K is a constant. The total energy of the particle will be:

1. $\frac{K}{2r}$

2. $-\frac{K}{2r}$

3. $-\frac{K}{r}$

4. $\frac{K}{r}$