The potential energy of a certain spring when stretched through a distance S is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through additional distance S will be

Question

The potential energy of a certain spring when stretched through a distance S is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through additional distance S will be (A) 30 (B) 40 (C) 10 (D) 20

Tardigrade Admin · Accepted Answer

U=(1/2) k S2=10 J ldots(i) U prime=(1/2) k(S+S)2=U((1/2) k S2)=40 J (Using (i)) ∴ W=U' - U = 40 J -10 J =30 J

Q. The potential energy of a certain spring when stretched through a distance $S$ is $10$ joule. The amount of work (in joule) that must be done on this spring to stretch it through additional distance $S$ will be

30

40

10

20

$U = \frac{1}{2} k S^{2} = 10 J \dots$ (i)
$U^{'} = \frac{1}{2} k (S + S)^{2} = U (\frac{1}{2} k S^{2}) = 40 J$ (Using (i))
$∴ W = U^{'} - U = 40 J - 10 J = 30 J$

Q. The potential energy of a certain spring when stretched through a distance S is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through additional distance S will be

30

40

10

20

U=21​kS2=10J…(i) U′=21​k(S+S)2=U(21​kS2)=40J (Using (i)) ∴W=U′−U=40J−10J=30J

Q. The potential energy of a certain spring when stretched through a distance $S$ is $10$ joule. The amount of work (in joule) that must be done on this spring to stretch it through additional distance $S$ will be

$U = \frac{1}{2} k S^{2} = 10 J \dots$ (i)
$U^{'} = \frac{1}{2} k (S + S)^{2} = U (\frac{1}{2} k S^{2}) = 40 J$ (Using (i))
$∴ W = U^{'} - U = 40 J - 10 J = 30 J$