A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $${1 \over 4}$$ times that of the bob and the length of the thread is increased by 1/3rd of the original length, then the time period of the simple harmonic oscillations will be :-
A
T
B
$${3 \over 2}$$T
C
$${3 \over 4}$$T
D
$${4 \over 3}$$T
Explanation
$$T = 2\pi \sqrt {l/g} $$
When bob is immersed in liquid
mgeff = mg $$-$$ Buoyant force
mgeff = mg $$-$$ v$$\sigma$$g ($$\sigma$$ = density of liquid)
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 1011 Pa, g = 9.8 m/s2]
A uniform heavy rod of weight 10 kg ms$$-$$2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $$\times$$ 1011 Nm$$-$$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.
$$\Delta l = {1 \over 2} \times {10^{ - 9}} = 5 \times {10^{ - 10}}$$ m
Option (d)
4
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MCQ (Single Correct Answer)
In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10$$-$$5 m and density 1.2 $$\times$$ 103 kgm$$-$$3 ? Take viscosity of liquid = 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2. (Neglect buoyancy due to air).