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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2002

MCQ (Single Correct Answer)
In a simple harmonic oscillator, at the mean position
A
kinetic energy is minimum, potential energy is maximum
B
both kinetic and potential energies are maximum
C
kinetic energy is maximum, potential energy is minimum
D
both kinetic and potential energies are minimum.

Explanation

$$K.E = {1 \over 2}k\left( {{A^2} - {x^2}} \right);\,\,\,U = {1 \over 2}k{x^2}$$
At the mean position $$x=0$$
$$\therefore$$ $$K.E. = {1 \over 2}k{A^2} = $$ Maximum and $$U=0$$
2

AIEEE 2002

MCQ (Single Correct Answer)
If a spring has time period $$T,$$ and is cut into $$n$$ equal parts, then the time period of each part will be
A
$$T\sqrt n $$
B
$$T/\sqrt n $$
C
$$nT$$
D
$$T$$

Explanation

Let the spring constant of the original spring be $$k.$$

Then its time period $$T = 2\pi \sqrt {{m \over k}} $$ where $$m$$ is the mass of oscillating body.
When the spring is cut into $$n$$ equal parts, the spring constant of one part becomes $$nk.$$ Therefore the new time period,

$$T' = 2\pi \sqrt {{m \over {nk}}} = {T \over {\sqrt n }}$$

Questions Asked from Simple Harmonic Motion

On those following papers in MCQ (Single Correct Answer)
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