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 acceleration due to gravity, the work required to pull the hanging part on the table is:

1. \(MgL\)

2. \(MgL/3\)

3. \(MgL/9\)

4. \(MgL/18\)

In the given figure, a man pulls the mass m with the help of a rope. Work done by the man against gravity when mass is lifted by 0.5 m is: (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

     
1. 50 J
2. 100 J
3. 25 J
4. Zero

A particle of mass 'm' is projected at an angle '$\mathrm{\alpha \text{'}}$ with the horizontal, with an initial velocity 'u'. The work done by gravity during the time it reaches its highest point is:

1. $u^2{\sin }^{2}a$

2. $\frac{m{u}^2{\cos }^2\alpha }{2}$

3. $\frac{m{u}^2{\sin }^2\alpha }{2}$

4. $-\frac{m{u}^2{\sin }^2\alpha }{2}$

What is the work done by gravity on block A in 2 seconds after the blocks are released? (Pulley is light)

1.  240 J

2.  200 J

3.  120 J

4.  24 J