Wires A and B are connected with blocks P and Q, as shown, the ratio of lengths radii and Young's modulus of wires A and B are r, 2r and 3r respectively (r is a constant). Find the mass of block P if ratio of increase in their corresponding length is `(1)/(6r^2)`. The mass of the block Q is 3M

Options

A. M
B. 3M
C. 6M
D. 9M

Answer

B

Explanation

`trianglel=(FL)/(AY)`
`((trianglel)_A)/((trianglel)_B)=((F_A)/(F_B))((L_A)/(L_b))((A_B)/(A_A))((Y_B)/(Y_A))`
`=((KM)/(3M))(r )((1)/(2r))^2((1)/(3r))=(K)/(36r^2)=(1)/(6r^2)` (given)
`K=6` Mass of block `P=6M`