Question

A uniform rod of mass M is hanged with two strings P and Q such that rod is horizontal. A mass m is connected by a light ideal string from the end of rod as shown. Then the maximum value of mass m upto which the string P remains tight is [Length of rod is (a + b)] :

• A. $\left[ \frac { a - b } { 2 b } \right] M$
• B. $\left[ \frac { a + b } { 2 b } \right] M$
• C.
• D. $\left[ \frac { a + b } { 2 a } \right] M$

Answer 1

Answer: (A)

$\left[ \frac { a - b } { 2 b } \right] M$

Answer 2

At maximum value of m, T_P ® 0

\ T_Q = (m + M) g … (1)

Now taking torque about centre of gravity of rod

T_Q × $\left[ \frac { a - b } { 2 } \right]$ = mg × $\left[ \frac { a + b } { 2 } \right]$

or (m + M) [a – b] = m[a + b]

$\frac { m + M } { m }$ = $\frac { a + b } { a - b }$

$1 + \frac { \mathrm { M } } { \mathrm { m } }$ = $\frac { a + b } { a - b }$ ̃ m = $\left[ \frac { a - b } { 2 b } \right] M$