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JEE Main 20179 AprilOnline
Exam
JEE Main
Year
2017
Date
9 April
Mode
Online
Subject
Physics
Chapter
Laws of Motion

JEE Main 2017 · 9 April · Online · Physics · Laws of Motion

The machine as shown has 2 rods of length 1m connected by a pivot...

The machine as shown has 22 rods of length 1m1m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a 2kg2kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

The machine as shown has 2 rods of length 1m connected by a pivot at the top. The end of one rod is connected to the

Options

  1. ASpeed which is 34th\dfrac{3}{4}th of that of the roller when the weight is 0.4m0 . 4m above the ground
  2. BConstant speed
  3. CDecreasing speed
  4. DIncreasing speed

Correct answer

C. Decreasing speed

Step-by-step solution

The machine as shown has 2 rods of length 1m connected by a pivot at the top. The end of one rod is connected to the

vA=dxdt=d[2lcos(θ)]dt=−2lsin(θ)dθdt{v}_{A} = \dfrac{d x}{d t} = \dfrac{d \left[2lcos\left(\theta\right)\right]}{d t} = - 2lsin\left(\theta\right)\dfrac{d \theta}{d t} and

Vertical velocity of BB, {v}_{B} = \dfrac{d y}{d t} = \dfrac{d \left[lsin\left(\theta\right)\right]}{d t} = lcos\left(\theta\right)\dfrac{d \theta}{d t}</p><p></p><p>\dfrac{{v}_{A}}{{v}_{B}} = - 2\tan \left(\theta\right) ⇒ {v}_{B} = - \dfrac{{v}_{A}\cot \left(\theta\right)}{2}<br/><br/><br /> <br />θ→\begin{array}{ll}\theta \to\end{array}increase</p><p>increase</p><p>cot\theta \todecrease</p><p>Hence,∣vB∣→decrease</p><p>Hence, \left|{v}_{B}\right| \todecrease.

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