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

Answer 1

The correct option is A $\frac{T}{M+m-\frac{ml}{L}}-g$

Let the acceleration of the lift be ${}^{\prime }{a}^{\prime }$
Mass of the lower portion of the string is $m\frac{(L-l)}{L}$
Now using newton's 2nd law
$F_{\text{net}}=m_{system}a$
$\Rightarrow T-Mg-\frac{m(L-l)}{L}g=[M+\frac{m(L-l)}{L}]a$
$\Rightarrow a=\frac{T}{M+m\frac{(L-l)}{L}}-g$