A ‘T’ shaped object with dimensions shown in the figure, is

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 Multiple Choice QuestionsMultiple Choice Questions

21.

Angular momentum of the particle rotating with a central force is constant due to

  • Constant Force

  • Constant linear momentum

  • Zero Torque

  • Zero Torque

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22.

A force of negative straight F straight k with hat on top acts on O, the origin of the coordinate system. The torque about the point (1, −1) is

  • negative straight F left parenthesis straight i with hat on top space minus straight j with hat on top right parenthesis
  • straight F left parenthesis straight i with hat on top space minus straight j with hat on top right parenthesis
  • negative straight F left parenthesis straight i with hat on top space plus straight j with hat on top right parenthesis
  • negative straight F left parenthesis straight i with hat on top space plus straight j with hat on top right parenthesis
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23.

A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω′

  • fraction numerator ωm over denominator left parenthesis straight m plus 2 straight M right parenthesis end fraction
  • fraction numerator straight omega space left parenthesis straight m space plus space 2 straight M right parenthesis over denominator straight m end fraction
  • fraction numerator straight omega space left parenthesis straight m minus 2 straight M right parenthesis over denominator left parenthesis straight m plus 2 straight M right parenthesis end fraction
  • fraction numerator straight omega space left parenthesis straight m minus 2 straight M right parenthesis over denominator left parenthesis straight m plus 2 straight M right parenthesis end fraction
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24.

The rms value of the electric field of the light coming from the Sun is 720 N/C. The average total energy density of the electromagnetic wave is

  • 3.3 × 10−3 J/m3

  • 4.58 × 10−6 J/m3

  • 6.37 × 10−9 J/m3

  • 6.37 × 10−9 J/m3

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25.

Four point masses, each of value m, are placed at the corners of a square ABCD of side A. The moment of inertia through A and parallel to BD is

  • m

  • 2m

  • √m

  • √m

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26.

A wire elongates by 

  • 2

  • 2

210 Views

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27.

A ‘T’ shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

  • 2

  • 3

  • 4

  • 4


C.

4

The point P must be the centre of mass of the T-shaped object since the force F does not produce any rotational motion of the object. So, we have to find the distance of the centre of mass from the point C.

The horizontal part of the T-shaped object has length L. If the mass of the horizontal portion is ‘m’, the mass of the vertical portion of the T- shaped object is 2m since its length is 2L. For finding the centre of mass of the T shaped object, it is enough to consider two point masses m and 2m located respectively at the midpoints of the horizontal and vertical portions of the T.

Therefore, the T-shaped object reduces to two point masses m and 2m at distances 2L and L respectively from the point C. The distance ‘r’ of the centre of mass of the system from the point C is given by

r = (m1r1 + m2r2)/(m1 + m2) = (m×2L + 2m×L)/(m + 2m) = 4L/3

[ Note that we have used the equation, r = (m1r1 + m2r2)/(m1 + m2) for the position vector r of the centre of mass in terms of the position vectors r1 and r2 of the point masses m1 and m2. We could use the simple equation involving the distances from C since the points are collinear].

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28.

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:

  • T Rn/2

  • T R3/2 for any n

  • TRn2+1

  • T Rn+12


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29.

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagadro number = 6.02 × 1023 gm mole–1)

  • 5.5 N/m

  • 6.4 N/m

  • 7.1 N/m

  • 2.2 N/m


30.

A wheel rotating at 12 rev/sis brought to rest in 6 s. The average angular deceleration in rad/s2 of the wheel during this process is

  • 4 π

  • 4

  • 72

  • 1/π


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