Calculation for Varying Direction

Q.

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at 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 its velocity as it reaches a position where the string is horizontal is

1. $\sqrt{u^2-2gL}$

2. $\sqrt{2gL}$
   

3. $\sqrt{u^2-gL}$

4. $\sqrt{2(u^2-2gL)}$

Q. A ball of mass $100\text{g}$ is under a force which causes a displacement $S$ in metres, given by the relation $S=t^3+t^2$ where $t$ is in seconds. Work done by the force in 3 seconds

1. $72.45\text{J}$
2. $36.55\text{J}$
3. $20\text{J}$
4. $54.45\text{J}$

Q. A ball of mass $100\text{g}$ is under a force which causes a displacement $S$ in metres, given by the relation $S=t^3+t^2$ where $t$ is in seconds. Work done by the force in 3 seconds

1. $72.45\text{J}$
2. $36.55\text{J}$
3. $20\text{J}$
4. $54.45\text{J}$

Q. Statement I :A small block of mass m is projected with some speed from point A on a smooth vertical tube track of small diameter as shown in Fig. 8.210. The vertical heights of points B and C from point of projection are $h_{B}and{h}_C$ such that $h_B=2h$ and $h_C=h.$ Then the minimum possible speed of the block at point C is $\sqrt{2gh}$ (where g is acceleration due to gravity).

Statement II . The minimum speed of the block at point C in situation given in Statement I depends on $h_B-h_C.$

1. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
2. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
3. Statement I is true, Statement II is false
4. Statement I is false, Statement II is true