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Solve the following :

Question:

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

Solution:

a) pseudo force acts downward

$\Rightarrow T=m\left(a_{0}+g\right)=0.05(1.2+9.8)=0.55 \mathrm{~N}$

b) $F_{p}\left(\right.$ psend ${ }^{\theta}$ force) acts downward, but $a_{0}=-v e$

$\Rightarrow \mathrm{T}=\mathrm{m}\left(-\mathrm{a}_{0}+\mathrm{g}\right)=0.05(-1.2+9.8)=0.43 \mathrm{~N}$

(c) $F_{b}=0$ as $a_{0}=0=>T=m g=0.05 \times 9.8=0.49 \mathrm{~N}$

d) $F_{0}$ acts upward $=>T=m\left(-a_{0}+g\right)=0.43 N$

e) $F_{p}$ acts upward but a=-ve

$\mathrm{T}=\mathrm{m}\left(-\left(-\mathrm{a}_{0}\right)+\mathrm{g}\right)$

$=0.05(1.2+9.8)=0.55 \mathrm{~N}$

f) $F_{p}=0$ as a $a_{0}=0$

$\Rightarrow \mathrm{T}=\mathrm{mg}=0.49 \mathrm{~N}$

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