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

Potential Energy Formulae

Two similar s...

Question

Two similar springs $P$ and $Q$ have spring constants $k_{P}$ and $k_{Q}$ , such that $k_{P} > k_{Q}$ . They are stretched, first by the same amount (case a ), then by the same force (case b ). The work done by the springs $W_{P}$ and $W_{Q}$ are related as, in case (a) and case (b), respectively

W_{P} = W_{Q}; W_{P} > W_{Q}

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

W_{P} = W_{Q}; W_{P} = W_{Q}

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

W_{P} > W_{Q}; W_{Q} > W_{P}

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

W_{P} < W_{Q}; W_{Q} < W_{P}

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

Open in App

Solution

The correct option is C $W_{P} > W_{Q}; W_{Q} > W_{P}$
Given, $K_{P} > K_{Q}$
In case (a), the elengation is same
i.e., $x_{1} = x_{2} = x$
So, $W_{P} = \frac{1}{2} K_{P} x^{2}$ and $W_{Q} = \frac{1}{2} K_{Q} x^{2}$
$∴ \frac{W_{P}}{W_{Q}} = \frac{K_{P}}{K_{Q}} > 1 (K_{P} > K_{Q})$
$\Rightarrow W_{P} > W_{Q}$
In case (b), the spring force is same
i.e., $F_{1} = F_{2} = F$
So, $x_{1} = \frac{F}{K_{P}}, x_{2} = \frac{F}{K_{Q}}$
$∴ W_{P} = \frac{1}{2} K_{P} x_{1}^{2} = \frac{1}{2} K_{P} \frac{F^{2}}{K_{P}^{2}} = \frac{1}{2} \frac{F^{2}}{K_{P}}$
and $W_{Q} = \frac{1}{2} K_{Q} x_{2}^{2} = \frac{1}{2} K_{Q} . \frac{F^{2}}{K_{Q}^{2}} = \frac{1}{2} \frac{F^{2}}{K_{Q}}$
$∴ \frac{W_{P}}{W_{Q}} = \frac{K_{Q}}{K_{P}} < 1 \Rightarrow W_{P} < W_{Q}$

Suggest Corrections

Similar questions

Q. Two similar springs

P

and

Q

have spring constants

k_{P}

and

k_{Q}

, such that

k_{P} > k_{Q}

. They are stretched, first by the same amount (case a ), then by the same force (case b ). The work done by the springs

W_{P}

and

W_{Q}

K_{P}

and

K_{Q}

, such that

K_{P} > K_{Q}

. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the spring

W_{P}

and

W_{Q}

Two springs have their force constant as $k_{1}$ and $k_{2} (k_{1} > k_{2})$ . When they are stretched by the same force

Two springs A and B have force constants $k_{1}$ and $k_{2}$ respectively. The ratio of work done on A to that done on B when they are stretched by the same force is

Q. Two springs have force constants

k_{1}

and

k_{2} (k_{1} > k_{2})

. On which spring is more work done, if (i) they are stretched by the same force and (ii) they are stretched by same distance?

Join BYJU'S Learning Program

Explore more

Potential Energy Formulae

Standard XII Physics

Join BYJU'S Learning Program

Two similar springs P and Q have spring constants kP and kQ, such that kP>kQ. They are stretched, first by the same amount (case a ), then by the same force (case b ). The work done by the springs WP and WQ are related as, in case (a) and case (b), respectively

Two similar springs $P$ and $Q$ have spring constants $k_{P}$ and $k_{Q}$ , such that $k_{P} > k_{Q}$ . They are stretched, first by the same amount (case a ), then by the same force (case b ). The work done by the springs $W_{P}$ and $W_{Q}$ are related as, in case (a) and case (b), respectively