In two pulley-paricle systems (i) and (ii) , the acceleration and force imparted by the string on the pulley and tension in the strings are `(a_(1) ,a_(2))`, `(N_(1),N_(2))` and `(T_(1),(T_(2))`, respectively . Ignoring friction in all contacting surfaces, study the following statements:

(a) `(a_1)/(a_2)=1`
(b) `(T_1)/(T_2)lt1`
(c)`(N_1)/(N_2)gt1`
(d) `(a_1)/(a_2)lt1`
Now mark the correct answer:

Options

A. `A=a_(1)-a_(2)`
B. `A=a_(1)+a_(2)`
C. `A=(a_(1)-a_(2))/(2)`
D. `A=(a_(1)+a_(2))/(2)`

Answer

C

Explanation

(c ) `(x_(P)-x_(1))+(x_(P)-x_(2))`=length of string= constant
Differentiating twice with respect to time, we get

`a_(P)=(a_(1)+a_(2))/(2)`
Here `a_(P)=A,a_(1)` is positive and `a_(2)` is negative. Hence,
`A=(a_(1)-a_(2))/(2)`