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

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

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 $W_{Q}$ are related as, in case ( $a$ ) and case ( $b$ ) respectively [2015]

1 $W_{P} > W_{Q}$ $;$ $W_{Q} > W_{P}$

2 $W_{P} < W_{Q}$ $;$ $W_{Q} < W_{P}$

3 $W_{P} = W_{Q}$ $;$ $W_{P} > W_{Q}$

4 $W_{P} = W_{Q}$ $;$ $W_{P} = W_{Q}$

Ans.
(1)

Here, $K_{P} > K_{Q}$

Case (a) : Elongation ( $x$ ) in each spring is same.

$W_{P} = \frac{1}{2} K_{P} x^{2},$ $W_{Q} = \frac{1}{2} K_{Q} x^{2} ∴ W_{P} > W_{Q}$

Case (b) : Force of elongation is same.

So, $x_{1} = \frac{F}{K_{P}}$ and $x_{2} = \frac{F}{K_{Q}}$ ; $W_{P} = \frac{1}{2} K_{P} x_{1}^{2} = \frac{1}{2}$ $\frac{F^{2}}{K_{P}}$

$W_{Q} = \frac{1}{2} K_{Q} x_{2}^{2} = \frac{1}{2}$ $\frac{F^{2}}{K_{Q}} ∴ W_{P} < W_{Q}$

Solution

1 $W_{P} > W_{Q}$ $;$ $W_{Q} > W_{P}$

2 $W_{P} < W_{Q}$ $;$ $W_{Q} < W_{P}$

3 $W_{P} = W_{Q}$ $;$ $W_{P} > W_{Q}$

4 $W_{P} = W_{Q}$ $;$ $W_{P} = W_{Q}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. 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 [2015]

1 WP>WQ ; WQ>WP

2 WP<WQ ; WQ<WP

3 WP=WQ ; WP>WQ

4 WP=WQ ; WP=WQ

Ans. (1) Here, KP>KQ Case (a) : Elongation (x) in each spring is same. WP=12KPx2, WQ=12KQx2 ∴ WP>WQ Case (b) : Force of elongation is same. So, x1=FKP and x2=FKQ; WP=12KPx12=12F2KP WQ=12KQx22=12F2KQ ∴ WP<WQ

Want Us to Email you About Special Offers & Updates?

1 $W_{P} > W_{Q}$ $;$ $W_{Q} > W_{P}$

2 $W_{P} < W_{Q}$ $;$ $W_{Q} < W_{P}$

3 $W_{P} = W_{Q}$ $;$ $W_{P} > W_{Q}$

4 $W_{P} = W_{Q}$ $;$ $W_{P} = W_{Q}$