Two masses `M_(1)=5kg,M_(2)=10`kg are connected at the ends of an inextensible string passing over a frictionless pulley as shown. When masses are released, then acceleration of masses will be

Options

A. g
B. g/2
C. g/3
D. g/4

Answer

C

Explanation

Since `M_2 gt M_1` therefore `M_2` moves downwards and `M_1` moves upwards with and acceleration a as shown in the figure

the equation of motion for ` M_1 ` is ` T- M_1 g= M_1 a `
Free body diagram of `M_2`
the equation of motion for `M_2 ` is
` M_2 g - T = M_2 a `
Adding (i ) and (ii ) , we get
` a=( (M_2 -M_1)g)/(m_2 +M_1) = ((10-5 ) g)/((10+5 )= (g)/(3) `