AP EAPCET 04-Jul-2022 Shift 1 Paper

Given, height, h=1m
mass, m=1‌kg
spring constant, k=15Nm−1
The kinetic energy of mass after falling on the platform will be converted into potential energy of the spring.
Thus, mg(h+x)=‌

1

2

kx2
‌1×10(1+x)‌=‌

1

2

×15×x2
⇒‌10×‌

2

15

(1+x)‌=x2
⇒‌

4

3

(1+x)‌=x2
⇒‌4+4x‌=3x2
⇒3x2−4x−4‌=0
⇒3x2−6x+2x−4‌=0
⇒3x(x−2)+2(x−2)‌=0
⇒‌(x−2)‌=0
or ‌‌(3x+2)‌=0
‌x=2m or x‌=‌

−2

3

m
Since, x is the compression, which cannot be negative, thus x=2m.