Verified Solution • 2025–26 Session moderate

QJEEAdv21Ph9702: JEE Advanced 2021 Physics - Class 11 JEEAdv21Ph9702 Solution: One end of a horizontal uniform beam of weight W and length L…

One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight α\alpha W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2 2\sqrt 2 )W. Which of the following statement(s) is(are) correct?

JEE Advanced 2021 Paper 2 Online Physics - Impulse & Momentum Question 9 English

Multiple Choice Options

  • A The vertical component of reaction force at O does not depend on α\alpha
  • B The horizontal component of reaction force at O is equal to W for α\alpha = 0.5
  • C The tension in the rope is 2W for α\alpha = 0.5
  • D The rope breaks if α\alpha > 1.5

Step-by-Step Verified Solution

Free body diagram of rod

JEE Advanced 2021 Paper 2 Online Physics - Impulse & Momentum Question 9 English Explanation
∑Fx=0\sum {{F _x} = 0}

R1=Tcos⁡45∘{R_1} = T\cos 45^\circ

R1=T2{R_1} = {T \over {\sqrt 2 }} ..... (i)

∑Fy=0\sum {{F_y} = 0}

R2+Tsin⁡45∘=W+αW{R_2} + T\sin 45^\circ = W + \alpha W

R2+T2=W(1+α){R_2} + {T \over {\sqrt 2 }} = W(1 + \alpha ) ..... (ii)

∑τ0=0\sum {{\tau _0} = 0}

WL2+αWL=T2LW{L \over 2} + \alpha WL = {T \over {\sqrt 2 }}L

T=2W[α+12]T = \sqrt 2 W\left[ {\alpha + {1 \over 2}} \right] ..... (iii)

From Eqs. (ii) and (iii), we get

R2+W[α+12]=W(1+α){R_2} + W\left[ {\alpha + {1 \over 2}} \right] = W(1 + \alpha )

R2=W2{R_2} = {W \over 2}

Hence, option (a) is correct.

From Eqs. (i) and (iii), we get

R1=W[α+12]{R_1} = W\left[ {\alpha + {1 \over 2}} \right]

α\alpha = 0.5, R1 = W

Hence, option (b) is correct.

From Eq. (iii), if α\alpha = 0.5

T=2WT = \sqrt 2 W

Tmax⁡=22W{T_{\max }} = 2\sqrt 2 W

For rope to break,

T > 2\sqrt 2 W

\sqrt 2 W\left[ {\alpha + {1 \over 2}} \right] > 2\sqrt 2 W \Rightarrow \alpha > {3 \over 2}

Hence, option (d) is correct.

Related Learning Resources & Exam Preparation

JEE Advanced PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring