Question

A stick of mass m and length / is pivoted at one
end and is displaced through an angle 0.
The increase in potential energy is

please need full explanation , no copy paste ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Potential\:Energy=mgl(1-cos\:\theta)}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline{\bold{Given :}}} \\ \tt: \implies Mass \: of \: stick = m \\ \\ \tt: \implies Length \: of \: stick = l \\ \\ \tt: \implies Angle = \theta \\ \\ \red{\underline{\bold{To \: Find :}}} \\ \tt: \implies Increase \: potential \: energy =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies cos \: \theta = \frac{b}{h} \\ \\ \tt: \implies cos \: \theta = \frac{AB}{l} \\ \\ \tt: \implies AB = l \: cos \: \theta \\ \\ \bold{For \: height :} \\ \tt: \implies h = l - l \: cos \: \theta \\ \\ \tt: \implies h = l(1 - cos \: \theta) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Potential \: energy = mgh \\ \\ \tt: \implies Potential \: energy =mg \times l(1 - cos \: \theta) \\ \\ \green{ \tt: \implies Potential \: energy =mgl(1 - cos \: \theta)}$