Write down the number of significant figure in the following.
3.08 x 10¹¹

The refractive index of water is found to have the values 1.29,1.33,1.34,1.35,1.32,1.36,1.30 and 1.33.Calculate mean value of refractive index

Derive the dimensions formula of physical quantities. Velocity gradient

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 Å). Why is this ratio so large ?

Two resistors of resistance \({ R }_{ 1 }=\left( 100\pm 3 \right) \Omega \) and \({ R }_{ 2 }=\left( 200\pm 4 \right) \Omega \) are connected (i) in series, (ii) in parallel. Find the equivalent resistance of the series combination. Use for the relation R = R₁ + R₂.

Using a screw gauge, the diameter of a metal rod was measured. The observation are given as follows: 0.39 mm, 0.37 mm, 0.41 mm, 0.38 mm, 0.38 mm, 0.37 mm, 0.40 mm, 0.39 mm. Calculate the relative error.

The percentage error in A,B,C and D are 1%, 2%,4% and 2% , respectively.Find the percentage error in Q which is given by \(Q=\frac { { A }^{ 2 }.{ B }^{ \frac { 3 }{ 2 } } }{ { C }^{ 4 }.{ D }^{ \frac { 1 }{ 2 } } } \)

Find an expression for viscous force F acting on a tiny steel ball of radius r moving in a viscous liquid of viscosity \(\eta \) with a constant speed v by the method of dimensional analysis.

P.A.M. Dirac, a great physicist of 20th century found that from the following basic constants, a number having dimensions of time can be constructed:
(i) charge on electron (e),
(ii) permittivity of free space (e₀),
(iii) mass of electron (m_e),
(iv) mass of proton (m_p),
(v) speed of light (c),
(vi) universal gravitational constant (G).
Obtain Dirac's number, given that the desired number is proportional to m_p^-1 and m_e^-2What is the significance of this number?

A laser light beam sent to the moon takes 2.56 s to return after reflection at the Moon's surface. Calculate the radius of the lunar orbit around the earth.