Question

Two spherical bodies of mass M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

• A. 7.5 R
• B. 1.5 R
• C. 2.5 R
• D. 4.5 R

Answer 1

Answer: (A)

7.5 R

Answer 2

Hint: As per the hint, this question is about the attraction due to gravitational force. Hence, we will apply here the universal law of gravitation to get the answer.

Let's draw the observation as per the question asked:

Fig 1: distance covered by the smaller body before collision

From the figure mentioned above and the details mentioned in the question, we can see:

Distance between the centres of spheres =12R

At the time of the collision the distance between their centres = 3R

So the total distance travelled by both bodies = 12R - (2R + R) = 9R

Since the bodies move under mutual forces, the centre of mass will remain stationary so

m1x1 = m2x2
mx = 5 m(9R - x)
x = 45R - 5x
6x = 45 R
x = $\frac {45}{6}$ R
x = 7.5 R

So, the correct answer is 7.5R would be the distance covered by the smaller body before collision.