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 =2_(m_B)`
` (Gm_Am_B)/(d^(2)) = (Gm_Bm_C)/((d//2)^(2))`
` (2m_Bm_B)/(d^(2)) = (m_Bm_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 .`