Question

Calculate power generated by tension in the string in first $2$ seconds of motion.

• A. $250$ W
• B. $500$ W
• C. $750$ W
• D. $1000$ W

Answer 1

The correct option is C $750$ W

we see body moves upward direction hence, non-inertial frame so, use concept of pseudo force .

now $F$ is force acting on object

$F=m(g+a)$

where $a=\frac{g}{2}$ upward acceleration

$F=10(g+\frac{g}{2})=15g$

if $g=10\frac{m}{s^2}$

then ,

$F=150N$

instanteous velocity $\left(v\right)=u+at=0+\frac{gt}{2}$=$5t$

total distance covered within $0\le t\le 2$

$s=ut+\frac{1}{2g{t}^2}=\frac{1}{2g}\frac{1}{2t^2}=\frac{5}{2t^2}=\left(2.5\right)t^2$

now,

total energy = kinetic energy + potential energy

$\frac{1}{2}\times 10(5t{)}^2+10\times 10(2.5)t^2$

$=250t^2+125t^2$

$=375t^2$

now ,

$averagepower=\frac{totalenergy}{totaltimes}$

$=\frac{375t^2}{t}=375t$

now put $t=2$

Power $=375\times 2=750w$