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

Question

4 J of work is required to stretch a spring through 10 cm beyond its unstretched length. The extra work required to stretch it through additional 10 cm shall be (A) 4 J (B) 8 J (C) 12 J (D) 16 J

Tardigrade Admin · Accepted Answer

Total work done in increasing the length by l W=(1/2) (Y A/L) t2 or W propto l2 ∴ (W1/W2)=(l22/l22) Let the initial length be 10 . (4/W2) =(10 × 10/20 × 20) W2 =16 J

Q. $4 J$ of work is required to stretch a spring through $10 c m$ beyond its unstretched length. The extra work required to stretch it through additional $10 c m$ shall be

4 J

8 J

12 J

16 J

Total work done in increasing the length by $l$
$W = \frac{1}{2} \frac{Y A}{L} t^{2}$
or $W \propto l^{2}$
$∴ \frac{W _{1}}{W _{2}} = \frac{l _{2}^{2}}{l _{2}^{2}}$
Let the initial length be $10$ .
$\frac{4}{W _{2}} = \frac{10 \times 10}{20 \times 20}$
$W_{2} = 16 J$

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

4 J

8 J

12 J

16 J

Total work done in increasing the length by l W=21​LYA​t2 or W∝l2 ∴W2​W1​​=l22​l22​​ Let the initial length be 10 . W2​4​=20×2010×10​ W2​=16J

Q. $4 J$ of work is required to stretch a spring through $10 c m$ beyond its unstretched length. The extra work required to stretch it through additional $10 c m$ shall be

Total work done in increasing the length by $l$
$W = \frac{1}{2} \frac{Y A}{L} t^{2}$
or $W \propto l^{2}$
$∴ \frac{W _{1}}{W _{2}} = \frac{l _{2}^{2}}{l _{2}^{2}}$
Let the initial length be $10$ .
$\frac{4}{W _{2}} = \frac{10 \times 10}{20 \times 20}$
$W_{2} = 16 J$