Gravitational potential and potential energy — practice questions

Question 1 · 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 2 · 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 3 · 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 4 · 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 5 · 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 6 · 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 7 · 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 8 · 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 9 · difficulty L3 · understanding

A body of mass (2M) splits into four masses (m, M $$-$$ m, m, M $$-$$ m}, which are rearranged to form a square as shown in the figure. The ratio of $${M \over m}$$ for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ............ .

Question 10 · difficulty L3 · understanding

Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $$\sqrt {{a \over 7}{{GM} \over R}}$$ then the value of 'a' is ____________. [Given : The two planets are fixed in their position]