A pendulum bob of mass 50 g is suspended from the ceiling of an elevator. Find the tension in the string if the elevator (a) goes up with acceleration 1.2 $m/s^2$, (b) goes up with deceleration 1.2 $m/s^2$, (c) goes up with uniform velocity , (d) goes down with acceleration 1.2 $m/s^2$, (e) goes down with deceleration 1.2 $m/s^2$ and (f) goes down with unifrom velocity.

(a) The tension in the string is found out for the different conditions from the free diagram as shown below.

$T-(W+0.05\times 1.2)=0$

$\Rightarrow$ T $=0.05\times 9.8+0.05\times 9.8\times 1.2$

= 0.05 (9.8+ 1.2)

= 0.55 N

(b) Now,

$T+0.05\times 1.2-0.05\times 9.8=0$

$\Rightarrow T=0.05\times 9.8-0.05\times 1.2$

= 0.05 (9.8 -1.2)

= $0.05\times 8.6$

= 0.43 N

(c) When the elevator makes uniform motion,

T - W = 0

$\Rightarrow T=W=0.05\times 9.8=0.49N$

(d) $T+0.05\times 1.2-w=0$

$\Rightarrow T=w-0.05\times 1.2$

= 0.05 (9.8 - 1.2) = 0.43 N

(e) $T-(W+0.05\times 1.2)=0$

$\Rightarrow T=W+0.05\times 1.2$

= 0.05 (9.8+ 1.2) = 0.55 N

(f) When the elevator goes down with uniform velocity acceleration = 0.

$\therefore$ T - W = 0

$\Rightarrow T=W=0.05\times 9.8$

= 0.49 N