A ball of mass 4 kg, moving with a velocity of 10 ms -1, collides with a spring of length 8 m and force constant 100 Nm -1. The length of the compressed spring is x m. The value of x, to the nearest integer, is .

Question

A ball of mass 4 kg, moving with a velocity of 10 ms -1, collides with a spring of length 8 m and force constant 100 Nm -1. The length of the compressed spring is x m. The value of x, to the nearest integer, is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let's say the compression in the spring by:

y

. So, by work energy theorem we have

\Rightarrow \frac{1}{2} m v^{2} = \frac{1}{2} k y^{2}

\Rightarrow y = \frac{m}{k} \cdot v

\Rightarrow y = \frac{4}{100} \times 10

\Rightarrow y = 2 m

\Rightarrow

final length of spring

= 8 - 2 = 6 m

Q. A ball of mass 4kg, moving with a velocity of 10ms−1, collides with a spring of length 8m and force constant 100Nm−1. The length of the compressed spring is xm. The value of x, to the nearest integer, is ______.

Let's say the compression in the spring by: y. So, by work energy theorem we have ⇒21​mv2=21​ky2 ⇒y=km​​⋅v ⇒y=1004​​×10 ⇒y=2m ⇒ final length of spring =8−2=6m

Q. A ball of mass $4 k g$ , moving with a velocity of $10 m s^{- 1}$ , collides with a spring of length $8 m$ and force constant $100 N m^{- 1}$ . The length of the compressed spring is $x m$ . The value of $x$ , to the nearest integer, is ______.

Let's say the compression in the spring by: $y$ . So, by work energy theorem we have
$\Rightarrow \frac{1}{2} m v^{2} = \frac{1}{2} k y^{2}$
$\Rightarrow y = \frac{m}{k} \cdot v$
$\Rightarrow y = \frac{4}{100} \times 10$
$\Rightarrow y = 2 m$
$\Rightarrow$ final length of spring
$= 8 - 2 = 6 m$