Verified Solution • 2025–26 Session moderate

QJEEM25Ph29a3: JEE Main 2025 Physics - Class 11 JEEM25Ph29a3 Solution: A particle oscillates along the -axis according to the law,…

A particle oscillates along the xx -axis according to the law, x(t)=x0sin⁡2(t2)x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right) where x0=1 mx_0=1 \mathrm{~m} . The kinetic energy (K)(\mathrm{K}) of the particle as a function of xx is correctly represented by the graph

Multiple Choice Options

  • A https://ik.imagekit.io/novatra/photos/89a5d5b3239734e505cb1336998edd002fd6431d85ff816802fadf4d3cbeede6.webp
  • B https://ik.imagekit.io/novatra/photos/3ea6a408307e7dc06b6d3e229a4f8057aa402d13b0e3ecf1e8695fd197fbff78.webp
  • C https://ik.imagekit.io/novatra/photos/235a4c5526d476ed4469ed223e62b13c03902ae25745fedb4db576a8c86d796b.webp
  • D https://ik.imagekit.io/novatra/photos/d6cf5f5f4362d19fbf4255915b0cd39eb87694382a747bed3324123a2675bad3.webp

Step-by-Step Verified Solution

amp;x=x0sin⁡2t2=x0(1−cos⁡t2)amp;x−x02=−cos⁡t2amp; where x0=1amp;x−12=−cos⁡t2\begin{aligned}& x=x_0 \sin ^2 \frac{t}{2}=x_0\left(\frac{1-\cos t}{2}\right) \\& x-\frac{x_0}{2}=\frac{-\cos t}{2} \\& \text { where } x_0=1 \\& x-\frac{1}{2}=\frac{-\cos t}{2}\end{aligned}

Particle is oscillating between x=0\mathrm{x}=0 to x=1\mathrm{x}=1

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