JEE Advanced 2021 · Paper 2 · Physics Q1

← JEE Advanced 2021 · Paper 2

PhysicsMultiple correct+4 / -2Question 1 of 57

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 $\alpha W$ 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 $(2\sqrt2)W$ . Which of the following statement(s) is(are) correct?

A horizontal beam OP of length L and weight W hinged at O on a vertical wall. A rope runs from the free end P up to point Q on the wall, a height L above O (so the rope makes 45° with the beam). A block of weight αW hangs from P.

The vertical component of reaction force at

O

does not depend on

\alpha

The horizontal component of reaction force at

O

is equal to

W

for

\alpha = 0.5

The tension in the rope is

2W

for

\alpha = 0.5

The rope breaks if

\alpha > 1.5

Answer and worked solution

Official answer: A, B, D

Torque about the hinge O. The rope runs from P to Q, which is $L$ above O, so it makes $45^\circ$ with the beam:
$T\sin45^\circ\,L=W\frac L2+\alpha WL\implies T=\sqrt2\,W\left(\tfrac12+\alpha\right).$

Force balance. The rope pulls with horizontal and vertical components $T\cos45^\circ=T\sin45^\circ=W\left(\frac12+\alpha\right)$ .

Horizontal reaction at O: $H=W\left(\frac12+\alpha\right)$ .
Vertical reaction at O: $V=W+\alpha W-W\left(\frac12+\alpha\right)=\frac W2$ .

Check each option.

(A) $V=\frac W2$ does not depend on $\alpha$ . True.
(B) For $\alpha=0.5$ , $H=W$ . True.
(C) For $\alpha=0.5$ , $T=\sqrt2W$ , not $2W$ . False.
(D) The rope breaks when $T>2\sqrt2W$ , i.e. $\frac12+\alpha>2$ , i.e. $\alpha>1.5$ . True.

(A), (B), (D)

Topics:Equilibrium of rigid bodies Torque and rotational dynamics

Next question →

JEE Advanced 2021 · Paper 2, Physics question 1