Question

# Consider two solid spheres of radii $$R_1 = 1m, \, R_2 = 2m$$ and masses $$M_1$$ and $$M_2$$, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $$\dfrac{M_1}{M_2}$$ is: A
$$\dfrac{1}{6}$$
B
$$\dfrac{1}{3}$$
C
$$\dfrac{2}{3}$$
D
$$\dfrac{1}{2}$$
Solution
Verified by Toppr

#### Correct option is A. $$\dfrac{1}{6}$$Let $$E_1, E_2$$ be the gravitational field intensities on the surface of the two spheres. $$E_1 = \dfrac{GM_1}{R_1^2}$$ and $$E_2 = \dfrac{GM_2}{R_2^2}$$In a solid sphere, the gravitational field varies linearly from the center to the surface and is proportional to $$R^{-2}$$ outside the sphere.From the figure, we have $$E_1 = 2$$ at the surface of the first spher and $$E_2 = 3$$ at the surface of the second sphere.$$\therefore 2 = \dfrac{GM_1}{R_1^2} = \dfrac{GM_1}{1}, \, GM_1 = 2$$ ...(i)$$\therefore 3 = \dfrac{GM_2}{R_2^2} = \dfrac{GM_2}{2^2}, \, GM_2 = 12$$ ...(ii)Dividing (i) by (ii),$$\dfrac{M_1}{M_2} = \dfrac{2}{12} = \dfrac{1}{16}$$

12
Similar Questions
Q1

Two spheres of masses m1 and m2 (m1>m2) respectively are tied to the ends of a light, inextensible string which passes over a light frictionless pulley. When the masses are released from their initial state of rest, the acceleration of their centre of mass is: View Solution
Q2

Consider two masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that they complete circular motion in the same time t. The ratio of their untripetal acceleration is,

View Solution
Q3

Consider two solid spheres of radii R1=1 m,R2=2 m and masses m1 and m2, respectively. The gravitational field due to sphere 1 and 2 are shown. The value of m1m2 is: View Solution
Q4

Tow cars having masses m1 and m2 moves in circles of radii r1 and r2 respectively. If they complete the circle in equal time, the ratio of their angular speed ω12 is
(a) m1/m2
(b) r1/r2
(c) m1r1/m2/r2
(d) 1.

View Solution
Q5

Two satellites of masses m1 and m2 (m1>m2) are revolving around the earth in a circular orbit of radii r1 and r2 (r1>r2), respectively. Which of the following statements is true regarding their speeds ν1 and ν2

View Solution
Solve
Guides