BITSAT 2024 Shift 1 Paper

To find the speed of the mass just before it touches the spring, we begin by determining the spring constant, k, using Hooke's Law, where the force F is proportional to the compression x :
F=kx
Given that a force of 100 N compresses the spring by 1 m , the spring constant k is calculated as:
k=‌

F

x

=‌

100N

1m

=100N∕m
Next, we apply the principle of energy conservation. The initial potential and kinetic energy will equal the final potential energy stored in the compressed spring. The relevant energy conservation equation is:
‌

1

2

mv2+mgh=‌

1

2

kxmax2
where:
m is the mass of the block ( 10 kg ),
g is the acceleration due to gravity (10m∕ s2),
h is the vertical height change, which is the same as the compression in this scenario ( xmax=2m ),
v is the speed just before touching the spring,
x‌max ‌ is the maximum compression of the spring ( 2 m ).
Rearranging the equation for v gives:
v=√‌

kxmax2

m

−2gh
Substituting the known values:
v=√‌

(100N∕m)(2m)2

10‌kg

−2(10m∕ s2)(‌

2

2

)
This simplifies to:
v=√‌

(100)(4)

10

−40

v=√40−20=√20m∕ s
Thus, the speed of the mass just before it touches the spring is √20m∕ s