Question

A cabin is moving vertically upwards with an acceleration $a$. A massless string is attached to the ceiling of the cabin on which a bead of mass $m$ is sliding downwards with respect to string with an acceleration $a$. The tension in the string is

• A. $m(g-a)$
• B. $m(g=a)$
• C. $m(g+2a)$
• D. $mg$

Answer 1

The correct option is D $mg$

Let's say we observe the bead with respect to string. Now, the string itself is accelerated up with ${}^{\prime }{a}^{\prime }$
Hence, on the bead pseudo force $ma$ will act downward and it's acceleration is $a$ downward (with respect to string)
Let $T$ be the tension in the string
From FBD we have,
$ma+mg-T=ma$
$\Rightarrow T=mg$
Hence, option $\left(C\right)$ is correct.