A weightless thread can bear tension upto 37 N. A stone of mass 5

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 Multiple Choice QuestionsMultiple Choice Questions

241.

If a thin uniform wire of length X having linear mass density D is bent zero into a circular loop (as shown in the figure). What will be the moment of inertia of the loop about axis AB ?

   

  • 3 L2D/ 16 π

  • 2 L2D/ 3π

  • 3 L3D/ 8π2

  • 8 L2D/ 13π2


242.

A solid sphere rolls without slipping and presses a spring of spring constant k as shown in figure. Then, the compression in the spring will be

   

  • 2M3k

  • 2M5k

  • 5k7M

  • 7m5k


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243.

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms-2, then the maximum angular velocity of the stone will be

  • 2 rad s-1

  • 4 rad s-1

  • 8 rad s-1

  • 16 rad s-1


B.

4 rad s-1

Maximum tension in the thread is given by          Tmax = mg + mv2ror     Tmax   = mg + mrω2  ( v = )or           ω2 = Tmax - mgmrGiven,  Tmax = 37 N, m = 500g = 0.5 kg, g = 10 ms-2, r = 4m  ω2 = 37 - 0.5 × 100.5 × 4 = 37 - 52or   ω2 = 16or     ω = 4 rad s-1


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244.

A force-time graph for a linear motion of a body is shown in the figure. The change in linear momentum between O and 7 s is

  

  • 2 N-s

  • 3 N-s

  • 4 N-s

  • 5 N-s


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245.

Two blocks of equal masses m are released from the top of a smooth fixed wedge as shown in the figure. The acceleration of the centre of mass of the two blocks is

  • g

  • g2

  • 3g4

  • g2


246.

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge ofthe disc and normal to the disc is

  • MR2

  • 12MR2

  • 32MR2

  • 72MR2


247.

Moment of a couple is called

  • impulse

  • couple

  • torque

  • angular momentum


248.

A motor is rotating at a constant angular velocity of 500 rpm. The angular displacement per second is 

  • 350 π rad

  • 3π50 rad

  • 25 π3 rad

  • 50 π3 rad


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249.

If the length of the second's hand in a stop-clock is 3 cm, the angular velocity and linear velocity of the tip is

  • 0.2047 rad/s , 0.0314 ms-1

  • 0.2547 rad/s , 0.314 ms-1

  • 0.1472 rad/s , 0.06314 ms-1

  • 0.1047 rad/s , 0.00314 ms-1


250.

Three identical spheres, each ofmass 1 kg are kept as shown in figure below, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is

  • PQ + PR + QR3

  • PQ + PR3

  • PQ + QR3

  • PR + QR3


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