Three masses A, B and C are arranged as shown in the figure, the mass of 'A' is 2 times the mass of 'B' and the mass of B is 10 kg. If the force of attraction between A and B is equal to the force of attraction between B and C, then the mass of C is _________ kg.

Options

A. 10
B. 5
C. ` 2.5`
D. 2

Answer

B

Explanation

` F_(AB) = F_(BC), m_A = 2m_B`
` (Gm_Am_B)/(d^(2)) =(Gm_Bm_C)/((d//2) ^(2))`
` (2m_Bm_B)/(d^(2)) = (m_B m_C)/((d//2)^(2)) (therefore m_A = 2m_B)`
` (2m_B)/(d^(2)) = (m_C)/((d//2)^(2) ) rArr (2m_B)/(d^(2)) = (4m_C)/(d^(2))`
` 2m_B =4m_C,m_C = (2m_B)/(4) = (m_B)/(2) = (10)/(2) = 5 kg `