Which of the following pairs does not have same dimensions ?

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 Multiple Choice QuestionsMultiple Choice Questions

171.

If 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/sec. If radius of the path becomes 1 m, ther what will be the value of angular velocity?

  • 28.16 rad/sec

  • 19.28 rad/sec

  • 8.12 rad/sec

  • 35.26 rad/sec


172.

A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined plane. Which of the following will have maximum acceleration at the bottom of the plane?

  • Circular disc

  • Solid cylinder

  • Solid sphere

  • Hollow cylinder


173.

Calculate the heat emitted by a bulb of 100 W in 1 min.

  • 100 J

  • 1000 J

  • 600 J

  • 6000 J


174.

What is the moment of inertia for a solid sphere w.r.t. a tangent touching to its surface?

  • 2/5 MR2

  • 7/5 MR2

  • 2/3 MR2

  • 5/3 MR2


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175.

A cylindrical wire is twisted with an angle θ, what is torsion produced in it?

  • Cθ

  • Cθ2

  • 3/2


176.

Given  ω = 2 k^  and  r = 2 i^ + 2 j^. Find the linear velocity.

  • 4i^ + 4 j^

  • 4 i^ + 4 j^

  • -4 i^ + 4 j^

  • - 4 i^ - 4 j^


177.

What is moment of inertia of a cylinder of radius r, along its height?

  • mr2

  • mr2/2

  • 2 mr2/5

  • mr2/5


178.

Four holes of radius Rare cut from a thin square plate of side 4R and mass M. The moment of inertia of the remaining portion about z-axis is

 

  • π12 MR2

  • 43 - π4 MR2

  • 43 - π6 MR2

  • 83 - 10π16 MR2


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179.

Which of the following pairs does not have same dimensions ?

  • impulse and momentum

  • moment of inertia and moment of force

  • angular momentum and Planck's constant

  • work and torque


B.

moment of inertia and moment of force

Impulse  = F  ×  t

              = m ν2 - ν1t × t

               = m ( ν2 - ν1 )

Impulse =  change in momentum

∴ [ Impulse ] = [ Momentum ]

Angular momentum 

      L = m ν r

Planck's constant

  [h] = [energy] × [time]

⇒ [ F × r ×  time] = m ν2 - ν1t × r × t

⇒ m (ν2 - ν1 ) × r = ( change in momentum) × r

∴ [h] = [L]

Work

  W = F . d

Torque

  τ = r × F

∴  [W] = [ τ ]

Moment of inertia:- A measure of the resistance of a body to  angular acceleration about a given axis that is equal to the sum of each element of mass in the body and the square of the element's distance from the axis.  

 I = mr2

I = mass × (distance)2

Moment of force

  τ = r × F = distance × force

          = distance × change of momentumtime

∴ [ I ] ≠ [ τ ] 

Therefore, the moment of inertia and momentum of force have different dimensions.


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180.

Assertion:  A hollow shaft is found to be stronger than a solid shaft made of same material. 

Reason:  The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

  • If both assertion and reason are true and reason is the correct explanation of assertion

  • If both assertion and reason are true but reason is not the correct explanation of assertion

  • If assertion is true but reason is false

  • If both assertion and reason are false


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