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Oscillations

JEE Main 2025 (Online) 24th January Evening ShiftMCQMedium📈 Topic in 8% papers+4−1
Ques. 1JEE Main 2025, 24 January (Evening Shift)

A particle oscillates along the x-axis according to the law, x(t)=x0 2 ( t2 ) where x0=1 m. The kinetic energy (K) of the particle as a function of x is correctly represented by the graph

  1. [figure]
  2. [figure]
  3. [figure]
  4. [figure]

Answer

(4) [figure]

Solution

x= 1- t2 v= t2, and 2t=1-(1-2x)2=4x(1-x)

K= 12mv2= m8 2t= m2 x(1-x)

Downward parabola: K=0 at x=0,1 (extremes), maximum m8 at x= 12

[figure]

Answer: (4)

Keep practising — Oscillations

Ques. 2JEE Main 2025, 23 January (Morning Shift)

A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is y 10-2 s, where the value of y is (Acceleration due to gravity, g=10 m/s2, density of water =103 kg/m3 )

  1. 2
  2. 4
  3. 1
  4. 6
Ques. 3JEE Main 2025, 22 January (Evening Shift)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

  1. Both (A) and (R) are true and (R) is the correct explanation of (A)
  2. (A) is false but (R) is true
  3. (A) is true but (R) is false
  4. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

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