Direction using Vectors: Derivation

Q. A space station is set up in space at a distance equal to earth's radius from the surface of earth. Suppose a satellite can be launched from the space station also. Let $v_1$ and $v_2$ be the escape velocities of the satellite on the earth's surface and space station respectively, then

1. $v_2=v_1$
2. $v_2<v_1$
3. $v_2>v_1$
4. $1,2$ and $3$ are valid depending on the mass of satellite.

Q. A boy whirls a stone in a horizontal circle of radius $1.5\text{m}$ and at height $2.0\text{m}$ above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of $10\text{m}$. What is the magnitude of the centripetal acceleration of the stone during the circular motion?

1. $176.7{\text{m/s}}^2$
2. $166.7{\text{m/s}}^2$
3. $156.7{\text{m/s}}^2$
4. $146.7{\text{m/s}}^2$

Q. A stone is tied to a rope of length $2$ m and is whirled above his head horizontally by a man at a height of $9\text{m}$ from the ground. The stone covers a horizontal distance of $20\text{m}$ when the rope breaks. What is the magnitude of the centripetal acceleration when the stone was in the circular motion?

1. $111.11{\text{m/s}}^2$
2. $123.5{\text{m/s}}^2$
3. $99.25{\text{m/s}}^2$
4. $61.72{\text{m/s}}^2$

Q.

A stone dropped from a cliff on the surface of the Moon, reaches the surface of the moon in $30s$. If the acceleration due to gravity of the Moon is $1.63m{s}^{-2}$, calculate the velocity of the stone on touching the surface of the Moon?

Q. A wheel of radius 'r' rolls without slipping with a speed 'v' on a horizontal road. When it is at point 'A' on the road, a small lump of mud separates from the wheel at its highest point 'C' on the road. The distance AC will be:

1. $v\sqrt{\frac{r}{g}}$
2. $2v\sqrt{\frac{r}{g}}$
3. $4v\sqrt{\frac{r}{g}}$
4. $v\sqrt{\frac{3r}{g}}$

Q. Pop the bubbles containing quantities that doesn't change during uniform circular motion. If on standard symbol, vector sign is not included, then they represent only magnitude of that vector.

1. Speed
2. $w$
3. $\theta$
4. $\overrightarrow{V}$
5. $\alpha$
6. Time period
7. $\overrightarrow{a}$
8. Linear
   momentum
9. ${\overrightarrow{f}}_{centripetal}$
10. $r$

Q. A boy whirls a stone in a horizontal circle of radius $1.5\text{m}$ and at height $2.0\text{m}$ above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of $10\text{m}$. What is the magnitude of the centripetal acceleration of the stone during the circular motion?

1. $146.7{\text{m/s}}^2$
2. $166.7{\text{m/s}}^2$
3. $156.7{\text{m/s}}^2$
4. $176.7{\text{m/s}}^2$

Q. A boy whirls a stone of small mass in a horizontal circle of radius $1.5$ m and at height $2.9$ m above level ground. The string breaks and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of $10$ m. What is the magnitude of the centripetal acceleration of the stone while in circular motion?

1. $33m{s}^{-2}$
2. $63m{s}^{-2}$
3. $93m{s}^{-2}$
4. $113m{s}^{-2}$