An -particle experiences the following force due to a nucleus k -0 beginarray 1 l l 1 lvecF- frac kr- 2- if- - R-frac- K R - 3vec r - i i - e - R -lend array The correct potential energy diagram for the above force isA-B-C-D-

The correct option is C F=dU/dr⇒ U=∫ F.dr for r gt;R u= ∫k/r^2r̂.dr = kr^ 2+1/ 2+1=k/r at r=∞ , U→ 0; at r=R U=k/R for r lt;R u=∫_R^0 F.dr=∫_R^0 k/ ...

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Byju's Answer

Standard XII

Physics

Velocity of COM

An α-particle...

Question

An $α -$ particle experiences the following force due to a nucleus $(k > 0)$
$\begin{matrix} \to F = \frac{k}{r^{2}} & i f & r > R = \frac{- K}{R^{3}} \to r & i f & r < R \end{matrix}$
The correct potential energy diagram for the above force is

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Solution

The correct option is D
$F = \frac{d U}{d r} \Rightarrow U = \int - F . d r f o r r > R u = - \int \frac{k}{r^{2}}^r . d r = - k \frac{r^{- 2 + 1}}{- 2 + 1} = \frac{k}{r} a t r = \infty, U \to 0; a t r = R U = \frac{k}{R} f o r r < R u = \int_{R}^{0} - F . d r = \int_{R}^{0} - \frac{- k}{R^{3}} \to r = \frac{+ k}{R^{3}} \times \frac{r^{2}}{2} = \frac{k}{R^{3}} \frac{R^{2}}{2} = \frac{k}{2 R} a t r = 0, U = \frac{k}{2 R}$

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An α−particle experiences the following force due to a nucleus (k>0) →F=kr2ifr>R=−KR3→rifr<R The correct potential energy diagram for the above force is

The correct option is D F=dUdr⇒U=∫−F.drfor r>Ru=−∫kr2^r.dr=−kr−2+1−2+1=krat r=∞,U→0;at r=R U=kRfor r<Ru=∫0R−F.dr=∫0R−−kR3→r=+kR3×r22=kR3R22=k2Rat r=0,U=k2R

An $α -$ particle experiences the following force due to a nucleus $(k > 0)$
$\begin{matrix} \to F = \frac{k}{r^{2}} & i f & r > R = \frac{- K}{R^{3}} \to r & i f & r < R \end{matrix}$
The correct potential energy diagram for the above force is