Question

$4J$ of work is required to stretch a spring through $10cm$ beyond its unstreched length. The extra work required to stretch it through additional $10cm$ shall be

• A. $4J$
• B. $8J$
• C. $12J$
• D. $16J$

Answer 1

Answer: (C)

$12J$

W = 4J

X = 10cm = 0.1 m = ${10}^{-1}$

By Hook's law,

W = $\frac{1}{2}$k$x^2$_________eq1

4 = $\frac{1}{2}$ x k x 0.1 x 0.1

8 = k x ${10}^{-2}$

k = 800 N$m^{-1}$

Additional 10cm means 0.1 + 0.1 i.e 0.2

Therefore again by same law,

$w_1$ = $\frac{1}{2}$ x 800 x 4 x ${10}^{-2}$

$w_1$ = $16J$

AS we know,

w = $w_1$ - W

w = $12J$