As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant 2 Nm -1. If both are given velocity v in opposite directions, then maximum elongation of the spring is :

Question

As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant 2 Nm -1. If both are given velocity v in opposite directions, then maximum elongation of the spring is : (A) ( V /2 √2) (B) (v/2) (C) (v/4) (D) ( v /√2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e6729bbaebd5265df18371b585658eb3-.png" /> using energy conservation (1/2) mv 2 × 2=(1/2) kx 2 ⇒ (1/4) v 2=(1/2) × 2 × x 2 ∴ x =( v /2)

Q. As per the given figure, two blocks each of mass $250 g$ are connected to a spring of spring constant $2 N m^{- 1}$ . If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is :

$\frac{V}{2 2}$

$\frac{v}{2}$

$\frac{v}{4}$

$\frac{v}{2}$

using energy conservation
$\frac{1}{2} m v^{2} \times 2 = \frac{1}{2} k x^{2}$
$\Rightarrow \frac{1}{4} v^{2} = \frac{1}{2} \times 2 \times x^{2}$
$∴ x = \frac{v}{2}$

Q. As per the given figure, two blocks each of mass 250g are connected to a spring of spring constant 2Nm−1. If both are given velocity v in opposite directions, then maximum elongation of the spring is :

22​V​

2v​

4v​

2​v​

using energy conservation 21​mv2×2=21​kx2 ⇒41​v2=21​×2×x2 ∴x=2v​

Q. As per the given figure, two blocks each of mass $250 g$ are connected to a spring of spring constant $2 N m^{- 1}$ . If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is :

$\frac{V}{2 2}$

$\frac{v}{2}$

$\frac{v}{4}$

$\frac{v}{2}$

using energy conservation
$\frac{1}{2} m v^{2} \times 2 = \frac{1}{2} k x^{2}$
$\Rightarrow \frac{1}{4} v^{2} = \frac{1}{2} \times 2 \times x^{2}$
$∴ x = \frac{v}{2}$