NEET UG Rotational Motion & Gravitation: System of Particles and Rotational Motion – Chapter Test

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Difficulty: 10 medium · 10 hard

System of Particles and Rotational Motion MCQ questions with answers

The first 3 of 20 questions. Unlock the series for the rest, each with a solution.

1. Q1. A particle of mass 2 kg moves in a straight line with a constant speed of 3 m/s. The line of motion lies at a perpendicular distance of 4 m from a fixed origin O. The magnitude of the angular momentum of the particle about O is:

   2 kg द्रव्यमान का एक कण 3 m/s की नियत चाल से एक सरल रेखा में गति करता है। गति की रेखा एक स्थिर मूल बिंदु O से 4 m की लंबवत दूरी पर स्थित है। O के परितः कण के कोणीय संवेग का परिमाण है:

   • A. 12 kg·m²/s
   • B. 6 kg·m²/s
   • C. 48 kg·m²/s
   • D. 24 kg·m²/s
   Solution

   For a particle moving in a straight line, L = mvr⊥, where r⊥ is the perpendicular distance of the line from O. Hence L = 2 × 3 × 4 = 24 kg·m²/s (it remains constant throughout the motion).

   सरल रेखा में गतिमान कण के लिए L = mvr⊥, जहाँ r⊥, O से रेखा की लंबवत दूरी है। अतः L = 2 × 3 × 4 = 24 kg·m²/s (यह गति के दौरान नियत रहता है)।

2. Q2. Two point masses of 2 kg and 3 kg are placed on the x-axis at x = 0 and x = 5 m respectively. The x-coordinate of the centre of mass of this system is:

   2 kg और 3 kg के दो बिंदु द्रव्यमान x-अक्ष पर क्रमशः x = 0 और x = 5 m पर रखे गए हैं। इस निकाय के द्रव्यमान केंद्र का x-निर्देशांक है:

   • A. 3 m
   • B. 2 m
   • C. 3.5 m
   • D. 2.5 m
   Solution

   x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂) = (2×0 + 3×5)/(2+3) = 15/5 = 3 m.

   x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂) = (2×0 + 3×5)/(2+3) = 15/5 = 3 m।

3. Q3. Which of the following physical quantities has the same dimensional formula as torque?

   निम्नलिखित में से किस भौतिक राशि का विमीय सूत्र बल आघूर्ण के समान है?

   • A. Linear momentum / रैखिक संवेग
   • B. Power / शक्ति
   • C. Force / बल
   • D. Work / कार्य
   Solution

   Torque has dimensions [ML²T⁻²], which are identical to those of work (energy). Force is [MLT⁻²], power is [ML²T⁻³], and linear momentum is [MLT⁻¹].

   बल आघूर्ण का विमीय सूत्र [ML²T⁻²] है, जो कार्य (ऊर्जा) के समान है। बल [MLT⁻²] है, शक्ति [ML²T⁻³] है, और रैखिक संवेग [MLT⁻¹] है।

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