If $x$ $=$ $3$ $-4t^2$ $+$ $t^3$, then work done in the first 4s will be:
(Mass of the particle is 3 gram)
1.  384 mJ
2.  168 mJ
3.  192 mJ
4.  None of the above

The bob of a simple pendulum having length l, is displaced from the mean position to an angular position θ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. $\sqrt{2gl(1-\cos \theta )}$

2. $\sqrt{2gl(1+\cos }$ $\theta )$

3. $\sqrt{2gl}$ $\cos \theta$

4. $\sqrt{2gl}$

A child is sitting on a swing. Its minimum and maximum heights from the ground are \(0.75\) m and \(2\) m, respectively. Its maximum speed will be: (Take \(g=10\) m/s²)
1. \(10\) m/s
2. \(5\) m/s
3. \(8\) m/s
4. \(15\) m/s

A stone is tied to a string of length 'l' is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed 'u'. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is:

1. $\sqrt{u^2-g\ell }$

2. $u-\sqrt{u^2-2g\ell }$

3. $\sqrt{2\mathrm{g}\ell }$

4. $\sqrt{2({\mathrm{u}}^2-\mathrm{g}\ell )}$

A ball is thrown vertically upward. It has a speed of 10m/sec when it has reached one-half of its maximum height. How high does the ball rise? Take g = 10 m/s²:

1. 5m

2. 15m

3. 10 m

4. 20 m