A point particle of mass 0.5 ,kg is moving al | vedclass

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Question

(B)

When particle is projected towards right side of origin with velocity $v$, it must cross a potential barrier of $4 J$ to escape to infinity.

Vedclass · Accepted Answer

$2 \,ms ^{-1}$

Vedclass · Answer

(B)

When particle is projected towards right side of origin with velocity $v$, it must cross a potential barrier of $4 J$ to escape to infinity.

i.e. $\quad \frac{1}{2} m v^2 \geq 4 \Rightarrow \frac{1}{2} 	imes \frac{1}{2} 	imes v^2 \geq 4$

or $\quad v^2 \geq 16 \Rightarrow v \geq 4 \,ms ^{-1}$

But it is possible that kinetic energy of particle is less than $4 \,J$, then it is

reflected back towards left with same velocity $v$. Here, we are taking repulsion from field as elastic collision.

Then particle can escape to infinity from left side of origin when,

$\frac{1}{2} m v^2 \geq 1 \Rightarrow \frac{1}{2} 	imes \frac{1}{2} v^2 \geq 1 	ext { or } v \geq 2 \,ms ^{-1}$

Hence, $v_{\min }$ for escape is $2 \,ms ^{-1}$.

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