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Laws of Motion question

2022 · 27 Jul · Shift 2 · Q43
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  5. /2022 · 27 Jul · Shift 2 · Q43

Laws of Motion question

2022 · 27 Jul · Shift 2 · Q43

JEE MainPhysicsLaws of MotionMCQ+4 / −1
A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ\thetaθ. The magnitude of the contact force will be :
  1. A
    Mg
  2. B
    Mgcos⁡θ\mathrm{Mg} \cos \thetaMgcosθ
  3. C
    Mgsin⁡θ+Mgcos⁡θ\sqrt{\mathrm{Mg} \sin \theta+\mathrm{Mg} \cos \theta}Mgsinθ+Mgcosθ​
  4. D
    Mg⁡sin⁡θ1+μ\operatorname{Mg} \sin \theta \sqrt{1+\mu}Mgsinθ1+μ​
View written solutionFree

Correct answer: A

  1. Forces acting on the block

A block sliding down a rough incline experiences:

  • Weight: MgMgMg vertically downward
  • Normal reaction: NNN perpendicular to the plane
  • Friction: fff along the plane, opposite the motion

Since the block slides down with constant velocity, its acceleration is zero.


  1. Resolve forces along the incline

Component of weight along the incline: Mgsin⁡θMg\sin\thetaMgsinθ

Since acceleration is zero along the plane, Mgsin⁡θ=fMg\sin\theta = fMgsinθ=f


  1. Resolve forces perpendicular to the incline

Perpendicular component of weight: Mgcos⁡θMg\cos\thetaMgcosθ

So normal reaction is N=Mgcos⁡θN = Mg\cos\thetaN=Mgcosθ


  1. Find the contact force

The contact force is the resultant of normal reaction and friction, because both are contact forces.

So its magnitude is R=N2+f2R = \sqrt{N^2 + f^2}R=N2+f2​

Substitute: R=(Mgcos⁡θ)2+(Mgsin⁡θ)2R = \sqrt{(Mg\cos\theta)^2 + (Mg\sin\theta)^2}R=(Mgcosθ)2+(Mgsinθ)2​

R=Mgcos⁡2θ+sin⁡2θR = Mg\sqrt{\cos^2\theta + \sin^2\theta}R=Mgcos2θ+sin2θ​

R=MgR = MgR=Mg


  1. Correct option

A:Mg\boxed{A: Mg}A:Mg​


  1. Comparison with stored answer

Stored correct answer: AAA

Our derived answer is also AAA, so they agree.

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