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NEET PHYSICSLAWS OF MOTIONMedium

Question

A block A of mass m1m_1 rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m2m_2 is suspended. The coefficient of kinetic friction between the block and the table is μk\mu_k. When the block A is sliding on the table, the tension in the string is:

A

(m2+μkm1)gm1+m2\frac{(m_2 + \mu_k m_1)g}{m_1 + m_2}

B

(m2μkm1)gm1+m2\frac{(m_2 - \mu_k m_1)g}{m_1 + m_2}

C

m1m2(1+μk)gm1+m2\frac{m_1 m_2 (1 + \mu_k)g}{m_1 + m_2}

D

m1m2(1μk)gm1+m2\frac{m_1 m_2 (1 - \mu_k)g}{m_1 + m_2}

Step-by-Step Solution

  1. Free Body Diagram of Block B (m2m_2):
  • Forces acting are gravity (m2gm_2g) downwards and tension (TT) upwards.
  • Equation of motion: m2gT=m2am_2g - T = m_2a ... (i) (assuming acceleration aa downwards).
  1. Free Body Diagram of Block A (m1m_1):
  • Forces acting horizontally are tension (TT) towards the pulley and kinetic friction (fkf_k) opposing motion.
  • Vertical forces balance: N=m1gN = m_1g, so fk=μkN=μkm1gf_k = \mu_k N = \mu_k m_1g.
  • Equation of motion: Tfk=m1a    Tμkm1g=m1aT - f_k = m_1a \implies T - \mu_k m_1g = m_1a ... (ii).
  1. Solve for Acceleration (aa):
  • Adding (i) and (ii): m2gμkm1g=(m1+m2)am_2g - \mu_k m_1g = (m_1 + m_2)a.
  • a=g(m2μkm1)m1+m2a = \frac{g(m_2 - \mu_k m_1)}{m_1 + m_2}.
  1. Solve for Tension (TT):
  • Substitute aa into equation (ii): T=m1(a+μkg)T = m_1(a + \mu_k g).
  • T=m1[g(m2μkm1)m1+m2+μkg]T = m_1 \left[ \frac{g(m_2 - \mu_k m_1)}{m_1 + m_2} + \mu_k g \right].
  • T=m1gm1+m2[m2μkm1+μk(m1+m2)]T = \frac{m_1 g}{m_1 + m_2} [ m_2 - \mu_k m_1 + \mu_k(m_1 + m_2) ].
  • T=m1gm1+m2[m2μkm1+μkm1+μkm2]T = \frac{m_1 g}{m_1 + m_2} [ m_2 - \mu_k m_1 + \mu_k m_1 + \mu_k m_2 ].
  • T=m1gm1+m2[m2+μkm2]=m1m2g(1+μk)m1+m2T = \frac{m_1 g}{m_1 + m_2} [ m_2 + \mu_k m_2 ] = \frac{m_1 m_2 g (1 + \mu_k)}{m_1 + m_2}. (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, Section 5.9 Friction).

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from LAWS OF MOTION. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

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