Gravitational potential and potential energy — NEET & JEE Questions

Question 1 · difficulty L1 · recall

Gravitational potential at a point is gravitational potential energy per unit

• A. mass
• B. charge
• C. volume
• D. force

Question 2 · difficulty L2 · understanding

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $\left(R_e\right)$. The increase in potential energy will be $\_\_\_\_$ . ( $g$ is acceleration due to gravity at the surface of earth)

• A. $\frac{1}{2} m g R_e$
• B. $\frac{3}{4} m g R_e$
• C. $\frac{1}{4} m g R_e$
• D. $\frac{2}{3} m g R_e$

Question 3 · difficulty L2 · understanding

$$\text { Match the LIST-I with LIST-II }$$ List - I List - II A. $$\text { Gravitational constant }$$ I. $$\left[\mathrm{LT}^{-2}\right]$$ B. $$\text { Gravitational potential energy }$$ II. $$\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]$$ C. $$\text { Gravitational potential }$$ III. $$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$$ D. $$\text { Acceleration due to gravity }$$ IV. $$\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$$ Choose the correct answer from the options given below:

• A. A-IV, B-III, C-II, D-I
• B. A-II, B-IV, C-III, D-I
• C. A-I, B-III, C-IV, D-II
• D. A-III, B-II, C-I, D-IV

Question 4 · difficulty L2 · understanding

To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $$R_E, g=$$ acceleration due to gravity on the surface of earth):

• A. $$1 / 2 m g R_E$$
• B. $$4 m g R_E$$
• C. $$m g R_E$$
• D. $$2 m g R_E$$

Question 5 · difficulty L2 · understanding

Match List I with List II : LIST I LIST II A. Kinetic energy of planet I. $$-\mathrm{GMm} / \mathrm{a}$$ B. Gravitation Potential energy of sun-planet system II. $$\mathrm{GMm} / 2 \mathrm{a}$$ C. Total mechanical energy of planet III. $$\frac{\mathrm{Gm}}{\mathrm{r}}$$ D. Escape energy at the surface of planet for unit mass object IV. $$-\mathrm{GMm} / 2 \mathrm{a}$$ (Where $$\mathrm{a}=$$ radius of planet orbit, $$\mathrm{r}=$$ radius of planet, $$\mathrm{M}=$$ mass of Sun, $$\mathrm{m}=$$ mass of planet) Choose the correct answer from the options given below :

• A. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
• B. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
• C. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
• D. (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

Question 6 · difficulty L2 · understanding

If $$\mathrm{V}$$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

• A. $$\frac{3 \mathrm{~V}}{2}$$
• B. $$\frac{\mathrm{V}}{2}$$
• C. $$\frac{4}{3} \mathrm{~V}$$
• D. $$\mathrm{V}$$

Question 7 · difficulty L2 · understanding

A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R$$_e$$), the increase in potential energy will be : (g = acceleration due to gravity on the surface of Earth)

• A. $$\frac{1}{2}mgR_e$$
• B. $$3~mgR_e$$
• C. $$\frac{1}{3}mgR_e$$
• D. $$\frac{2}{3}mgR_e$$

Question 8 · difficulty L2 · understanding

Water falls from a 40 m high dam at the rate of 9 $$\times$$ 10 4 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is : (Take g = 10 ms $$-$$2 )

• A. 25
• B. 50
• C. 100
• D. 18

Question 9 · difficulty L2 · understanding

Inside a uniform spherical shell : (1) the gravitational field is zero (2) the gravitational potential is zero (3) the gravitational field is same everywhere (4) the gravitational potential is same everywhere (5) all of the above Choose the most appropriate answer from the options given below :

• A. (1), (3) and (4) only
• B. (5) only
• C. (1), (2) and (3) only
• D. (2), (3) and (4) only

Question 10 · difficulty L3 · understanding

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $${x \over 5}{{G{M^2}} \over R}$$ where x is __________ (Round off to the Nearest Integer) (M is the mass of earth, R is the radius of earth, G is the gravitational constant)