An explosion breaks a rock into three parts in a horizontal plane

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 Multiple Choice QuestionsMultiple Choice Questions

251.

The moment of inertia of a thin rod of mass M and length L, about an axis perpendicularto the rod at a distance L4from one end is

  • ML26

  • ML212

  • 7 ML224

  • 7 ML248


252.

If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take

  • 96 h

  • 48 h

  • 6 h

  • 1.5 h


253.

A shell of mass 10 kg is moving with a velocity of 10 ms-1 when it blasts and forms two parts of mass 9 kg and 1 kg respectively. If the 1st mass is stationary, the velocity of the 2nd is

  • 1 m/s

  • 10 m/s

  • 100 m/s

  • 1000 m/s


 Multiple Choice QuestionsShort Answer Type

254.

A circular disc rolls down on an inclined plane without slipping. What fraction of its total energy is translational ?


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255.

An infinite number of charges, each equal to q, are placed along the x-axis at x=1, x=2, x = 4, x=8 and so on. What is the potential at x = 0 due to this set of charges ?


 Multiple Choice QuestionsMultiple Choice Questions

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256.

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1 and the second part of mass 2 kg moves with 8 ms-1 speed. If the third part flies off with 4 ms-1 speed, then its mass is

  • 3 kg

  • 5 kg

  • 7 kg

  • 17 kg


B.

5 kg

We have, p1 + p2 + p3 = 0      P = mv 1 × 12i + 2 × 8j + p3 = 0     12i + 16j + p3 = 0                          p3 = - (12i + 16j)                           p3 = 122 + 162                                    = 144 + 256                                    = 20 kg-m/sNow,                 p3 = m3v3                    m3 = p3v3 = 204 = 5 kg  


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257.

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

               

  • 3g2L

  • gL

  • 2gL

  • 2g3L


258.

A solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its centre so that it starts sliding with an initial velocity v0. When it finally starts rolling without slipping the speed of its centre is

  • 27 v0

  • 37 v0

  • 57 v0

  • 67 v0


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259.

Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds ω1 : ω2 : ω3 is

             

  • 1 : 1 : 1

  • 2 : 2 : 1

  • 1 : 2 : 1

  • 1 : 2 : 2


260.

A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the centre of mass of the system from the origin is

  • equal to R

  • less than equal to R

  • greater than R

  • greater than equal to R


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