A car of mass 1000 kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is 45o, the speed of the car is 

  • 20 ms-1

  • 30ms-1

  • 5 ms-1

  • 5 ms-1


B.

30ms-1

The angle of banking

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The upper half of an inclined plane of the inclination straight theta is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by,

  • straight mu space equals space fraction numerator 1 over denominator tan space straight theta end fraction
  • straight mu space equals space fraction numerator 2 over denominator tan space straight theta end fraction
  • straight mu space equals space 2 space tan space straight theta
  • straight mu space equals space 2 space tan space straight theta


C.

straight mu space equals space 2 space tan space straight theta

The block will be stationary when,


mg sin straight theta . L =  mg cos 

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A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 rev/s2 is,

  • 25 N

  • 50 N

  • 78.5 N

  • 78.5 N


D.

78.5 N


Mass, m = 50 kg

Radius, r = 0.5 m
Angular acceleration, 
Torque produced by the tension in the string,

= T x R = T x 0.5 = T/2 Nm      ... (i)

We know,
T = 1α                                ... (2)

From equations (i) and (ii)


     
Therefore,

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Two sphere A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along the x -axis. After the collision, B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction

  • same as that of B

  • opposite to that of B

  • straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 half close parentheses space to space the space straight x space minus axis
  • straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 half close parentheses space to space the space straight x space minus axis

C.

straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 half close parentheses space to space the space straight x space minus axis

Here, Pi = m2vi +m2 x 0



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The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle straight theta without slipping and slipping down the incline without rolling is,

  • 5:7

  • 2:3

  • 2:5

  • 2:5


A.

5:7

A solid sphere rolling without slipping down an inclined plane is,

We have in this case,

For a sphere slipping down an inclined plane,

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