Two masses `M_1 and M_2` are accelerated uniformly on a frictionless surface as shown in figure. The ratio of the tensions `(T_1)/(T_2)`is

Options

A. `(M_1)/(M_2)`
B. `(M_2)(M_1)`
C. `((M_1 +M_2))/( M_2)`
D. `(M_1)/((M_1 +M_2))`

Answer

D

Explanation

Let a be the common acceleration of the system. The equations of motion of masses` M_1 and M_2` are
`T_1 =M_1 a `
`T_2 -T_1 = M_2 a `
Adding (i) and (ii), we get` T_2 = (M_1 + M_2)a`
`therefore (T_1)/( T_2) =(M_1 )/(M_1 +M_2)`