A system consists of 3 particles each of mass m located at points

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51.

A system consists of 3 particles each of mass m located at points (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are

  • (6,6)

  • (3,3)

  • (1,1)

  • (2,2)


D.

(2,2)

If 3 masses are equal ie,

     m1 = m2 = m3

then coordinate of the centre of mass

x,y = m1x1 + m2x2 + m3x3m1 + m2 + m3, m1y1 + m2y2 + m3y3m1 + m2 + m3        = m + 2m + 3m3m, m + 2m + 3m3m        = 6m3m, 6m3m        = 2,2


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52.

A wheel of moment of inertia 2.5 kg-m2 has an initial angular velocity of 40 rads-1. A constant torque of 10 Nm acts on the wheel. The time during which the wheel is accelerated to 60 rads-1 is 

  • 4 s

  • 6 s

  • 5 s

  • 2.5 s


53.

A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity ω. Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

  • M4m ω

  • MM + 4m ω

  • MM - 4m ω


54.

The angular velocity of a wheel increases from 100 rps to 300 rps in 10 s. The number of revolutions made during that time is

  • 600

  • 1500

  • 2000

  • 3000


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55.

Three identical spheres, each of mass 3 kg are placed touching each other with their centres lying on a straight line. The centres of the sphere are marked at P, Q and R respectively. The distance of centre of mass of system from P is

  • PQ+ QR + PR3

  • PQ + PR3

  • PQ + QR + PR9

  • PQ + PR9


56.

The position of a particle is given by r = i^ + 2j^ - k^ and its linear momentum is given by p = 3i^ + 4j^ - 2k^. Then its angular momentum, about the origin is perpendicular to

  • yz-plane

  • z-axis

  • y-axis

  • x-axis


57.

A sphere of mass m and redius r rolls on a horizontal plane without slipping with the speed u. Now, if it rolls up vertically, the maximum height it would attain will be

  • 3u24g

  • 5u22g

  • 7u210g

  • u22g


58.

If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

  • 3 h

  • 1.5 h

  • 6 h

  • 4 h


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59.

A stone of mass m tied to a string of length l is rotating along a circular path with constant speed v. The torque on the stone is

  • mlv

  • mvl

  • zero

  • mv2l


60.

The distance between the centres of carbon and oxygen atoms in the carbon monoxide molecule is 1.130 A. Locate the centre of mass of the molecule relative to the carbon atom

  • 5.428 A

  • 1.130 A

  • 0.6457 A

  • 0.3260 A


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