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QJEEM22Phf559: JEE Main 2022 Physics - Class 11 JEEM22Phf559 Solution: Two bodies of masses and are connected by a light string going…

Two bodies of masses m1=5 kgm_{1}=5 \mathrm{~kg} and m2=3 kgm_{2}=3 \mathrm{~kg} are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m1\mathrm{m}_{1} will be : [Take g=10 ms−2]\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]

JEE Main 2022 (Online) 29th July Evening Shift Physics - Laws of Motion Question 42 English

Multiple Choice Options

  • A 30 N
  • B 40 N
  • C 50 N
  • D 60 N

Step-by-Step Verified Solution

JEE Main 2022 (Online) 29th July Evening Shift Physics - Laws of Motion Question 42 English Explanation

Force on equilibrium, m2g=m1gsin⁡θm_{2} g=m_{1} g \sin \theta

⇒m2=m1sin⁡θ\Rightarrow m_2=m_1 \sin \theta

⇒\Rightarrow sin⁡θ=m2m1=35\sin \theta=\frac{m_2}{m_1}=\frac{3}{5}

Normal force on m1, R=m1gcos⁡θR=m_{1} g \cos \theta

⇒Rm2g=cot⁡θ\Rightarrow \frac{R}{m_{2} g}=\cot \theta

⇒R=3×10×cot⁡θ=3×10×43(∵sin⁡θ=35)\Rightarrow R=3 \times 10 \times \cot \theta=3 \times 10 \times \frac{4}{3} \quad\left(\because \sin \theta=\frac{3}{5}\right)

⇒R=40\Rightarrow R=40 N

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