Assume that the displacement(s) of air is proportional to the pressure difference ($$\Delta $$p) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ($$\rho $$) and the frequency (f). If $$\Delta $$p ~ 10 Pa, v ~ 300 m/s, $$\rho $$ ~ 1 kg/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1) :

A wheel is rotating freely with an angular speed $$\omega $$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm with a separation of 10 cm.
The distance between an object and the objective lens, at which the strain on the eye is minimum is $${n \over {40}}$$ cm. The value of n is _____.

Two concentric circular coils, C₁ and C₂ are
placed in the XY plane. C₁ has 500 turns, and
a radius of 1 cm. C₂ has 200 turns and radius
of 20 cm. C₂ carries a time dependent current
I(t) = (5t² – 2t + 3) A where t is in s. The emf
induced in C₁ (in mV), at the instant t = 1 s is
$${4 \over x}$$. The value of x is ___ .