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PART - 1 CH - 5Work, Energy and Power — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsPART - 1 CH - 5Work, Energy and Power2 Marks
Question
A spring whose force constant is $k$ obeys Hooke's is law 4 J of work is required by pulling it to a length of 10 cm from the original length. Calculate :(i) Value of k
(ii) Additional work required to stretch the spring by additional 10 cm length.
✓

Answer

 (i)
$w =\frac{1}{2} k x^2$
$ \therefore \quad k=\frac{2 w}{x^2}$
It is given
$\begin{aligned}
w & =4 J \\
x & =10 cm=0.1 m \\
k & =\frac{2 \times 4}{(0.1)^2}=\frac{8}{0.01}=800 N / m
\end{aligned}$
(ii) Total work in pulling the spring by 20 cm
$\begin{aligned}
w & =\frac{1}{2} k x^2 \\
& =\frac{1}{2} \times 800 \times(0.2)^2
\end{aligned}$
$\begin{aligned}
w & =400 \times 0.04 \\
& =16 J
\end{aligned}$
Additional work $=16-4=12 J \quad \text { Ans. }$

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