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Q. No.A particle is moving in a circle of radius \(r\) under the action of a force \( F = α r^ 2 \) which is directed towards centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is:
(take potential energy \({=0}\) for \({r = 0)}\)
1. \({1\over 2}{\alpha r^3}\)
2. \({5\over 6}{\alpha r^3}\)
3. \({4\over 3}{\alpha r^3}\)
4. \({\alpha r^3}\)
(take potential energy \({=0}\) for \({r = 0)}\)
1. \({1\over 2}{\alpha r^3}\)
2. \({5\over 6}{\alpha r^3}\)
3. \({4\over 3}{\alpha r^3}\)
4. \({\alpha r^3}\)
Subtopic: Potential Energy: Relation with Force |
From NCERT
JEE
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A particle is moving along a circular path with a radius \(a,\) under the influence of an attractive force. The potential energy associated with the particle is given by: \(U=-\dfrac{k}{2r^2}.\)
The attractive force acting on the particle is:
| 1. | \(\dfrac{k}{4a^3}\) | 2. | \(\dfrac{k}{2a^3}\) |
| 3. | \(\dfrac{k}{a^3}\) | 4. | \(\dfrac{3k}{2a^3}\) |
Subtopic: Potential Energy: Relation with Force |
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If the potential energy between two molecules is given by \(U = -\dfrac{A}{r^6}+ \dfrac{B}{r^{12}}\),
then the potential energy at equilibrium separation between molecules is:
| 1. | \(\dfrac{-A^{2}}{2B}\) | 2. | \(\dfrac{-A^{2}}{4B}\) |
| 3. | \(0\) | 4. | \(\dfrac{-A^{2}}{3B}\) |
Subtopic: Potential Energy: Relation with Force |
64%
From NCERT
JEE
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Potential energy as a function of \({r}\) is given by; \({U}=\dfrac{{A}}{{r}^{10}}-\dfrac{{B}}{{r}^5},\) where \({r}\) is the interatomic distance, and \({A}\) and \({B}\) are positive constants. The equilibrium distance between the two atoms will be:
| 1. | \(\left ( \dfrac{{A}}{{B}}\right )^{1/5}\) | 2. | \(\left ( \dfrac{{B}}{{A}}\right )^{1/5}\) |
| 3. | \(\left ( \dfrac{{2A}}{{B}}\right )^{1/5}\) | 4. | \(\left ( \dfrac{{B}}{{2A}}\right )^{1/5}\) |
Subtopic: Potential Energy: Relation with Force |
81%
From NCERT
JEE
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The potential energy function corresponding to a conservative force is given as \(U(x, y, z)=\frac{3 x^2}{2}+5 y+6 z,\) then the force at \({x}=6\) is \(P~\text{N}.\) The value of \(P\) up to its nearest integral value is:
1. \(20\)
2. \(40\)
3. \(30\)
4. \(60\)
1. \(20\)
2. \(40\)
3. \(30\)
4. \(60\)
Subtopic: Potential Energy: Relation with Force |
53%
From NCERT
JEE
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