Question

An elevator accelerates upwards at a constant rate. A uniform string of length $L$ and mass $m$ supports a small block of mass M that hangs from the ceiling of the elevator. The tension at distance $l$ from the ceiling is $T$. The acceleration of the elevator is :

• A. $\frac{ T }{ M + m -\frac{ m l}{ L }}- g$
• B. $\frac{ T }{2 M + m -\frac{ ml }{ L }}+ g$
• C. $\frac{ T }{ M +\frac{ ml }{ L }}- g$
• D. $\frac{ T }{2 M - m +\frac{ ml }{ L }}- g$

Answer 1

Answer: (A)

Let $a$ be the acceleration of the lift.
Mass of lower portion of string
$=\frac{ m }{ L }( L -l)$
$\therefore T - Mg -\frac{ mg }{ L }( L -l)=\left( M +\frac{ m }{ L }( L -l)\right) a $
$\therefore a =\frac{ T }{ M + m -\frac{ m l}{ L }}- g$