Two springs A and B are identical except that A is stiffer than B i-e- k-A gt- k-B- nbsp- If the two springs are stretched by the same force- then

Given springs are stretched by the same force. We know that F = k x and given nbsp;k_A gt; k_B ∴ F = k_A x_A = k_B x_B......(1) Since W_A = 12k_A x_A^2 ; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Work Done: Spring

Two springs A...

Question

Two springs A and B are identical except that A is stiffer than B i.e., $k_{A} > k_{B}$ . If the two springs are stretched by the same force, then

More work is done on B, i.e.,

W_{B} > W_{A}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

More work is done on A, i.e.,

W_{A} > W_{B}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Work done on A and B are equal

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Work done depends on the way in which they are stretched

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A More work is done on B, i.e., $W_{B} > W_{A}$
Given springs are stretched by the same force.
We know that $F = k x$ and given $k_{A} > k_{B}$
$∴ F = k_{A} x_{A} = k_{B} x_{B}$ ......(1)
Since $W_{A} = \frac{1}{2} k_{A} x_{A}^{2}; W_{B} = \frac{1}{2} k_{B} x_{B}^{2}$
$\frac{W_{A}}{W_{B}} = \frac{k_{A} x_{A}^{2}}{k_{B} x_{B}^{2}}$
$\Rightarrow \frac{W_{A}}{W_{B}} = \frac{k_{A}}{k_{B}} {(\frac{k_{B}}{k_{A}})}^{2}$
$(from eqn (1), \frac{x_{A}}{x_{B}} = \frac{k_{B}}{k_{A}})$
$∴ \frac{W_{A}}{W_{B}} = \frac{k_{B}}{k_{A}}$
Because $k_{A} > k_{B}, W_{B} > W_{A}$

Suggest Corrections

Similar questions

Q. Two springs A and B are identical except that A is stiffer than B i.e.,

k_{A}

k_{B}

. If the two springs are stretched by the same force, then

Q. Two springs

A

and

B

are identical but

A

is harder than

B (k_{A} > k_{B})

. On which spring more work will be done if: (a)They are stretched through the same distance (b)They are stretched by same force?

Q. There are two massless springs A and B of spring constant

K_{A}

and

K_{B}

respectively and

K_{A} > K_{B}

. If

W_{A}

and

W_{B}

be denoted as work done on A and work done on B respectively, then

Q. Two springs

A

and

B

are identical but

A

is harder than

B (k_{A} > k_{B})

. Let

W_{A}

and

W_{B}

represent the work done when the springs are stretched through the same of the distance and

W_{A}^{'}

and

W_{B}^{'}

are the work done when these are stretched by equal forces then which of the following is true:

There are two mass less spring A and B of spring constant $K_{A}$ and $K_{B}$ respectively and $K_{A}$ > $K_{B}$ If $W_{A}$ and $W_{B}$ be denoted as work done on A and work done on B respectively, then

Join BYJU'S Learning Program

Two springs A and B are identical except that A is stiffer than B i.e., kA>kB. If the two springs are stretched by the same force, then

The correct option is A More work is done on B, i.e., WB>WAGiven springs are stretched by the same force. We know that F=kx and given kA>kB ∴F=kAxA=kBxB......(1) Since WA=12kAx2A;WB=12kBx2B WAWB=kAx2AkBx2B ⇒WAWB=kAkB(kBkA)2 (from eqn (1),xAxB=kBkA) ∴WAWB=kBkA Because kA>kB,WB>WA

Two springs A and B are identical except that A is stiffer than B i.e., $k_{A} > k_{B}$ . If the two springs are stretched by the same force, then