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The MCQs below are drawn from the Physics subject category.
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401
The wavelength associated with a moving particle depends upon power p of its mass m, qth power of its velocity v and rth power of Planck's constant h. Then the correct set of values of p, q and r is
Planck's constant has dimensions of energy × time: [M L^2 T^-2]×[T] = [M L^2 T^-1].
404
If K represents kinetic energy, V represents velocity and T represents time, and these are chosen as the fundamental units, then the dimensional formula of surface tension is
A Bose–Einstein condensate is characterized by a macroscopic number of bosons occupying the ground state when temperature is below the critical temperature T_c, so option A is correct.
406
188. Moment of inertia of a circular wire of mass M and radius R about its diameter is
For a thin circular ring, I_about diameter = (1/2) M R^2 by standard moment of inertia relations.
407
A fly-wheel rotating about a fixed axis has a kinetic energy of 380 Joule when its angular speed is 30 rad/s. The moment of inertia of the fly-wheel about the axis of rotation is
KE = 1/2 I ω^2 → I = 2 KE / ω^2 = 760 / 900 ≈ 0.844 ≈ 0.8 kg·m^2.
408
The moment of inertia of a circular ring about an axis passing through its centre and normal to its plane is 200 gm·cm^2. Then its moment of inertia about a diameter is
By the perpendicular axis theorem for a planar ring I_z = I_x + I_y and I_x = I_y, so 200 = 2I_diameter ⇒ I_diameter = 100 gm·cm^2.
409
The moment of inertia of a uniform semi-circular wire of mass M and radius R about a line perpendicular to the plane of the wire and passing through the centre is
For a thin wire at constant radius R the moment of inertia is I = R^2 ∑dm = M R^2, same as a full ring scaled by total mass.
410
The root mean square distance of 5 identical particles of masses, 1 g each, and distributed along OX is 6 cm (from O). The total moment of inertia about OY is
