1. a star is observed from two diametrically opposite points P & Q on earth , the angle 'x' subtended at the star by the two directions of observations is 1 degree 54 minutes . given the radius of earth 0.638x10 raised to 7.compute the distance of the star from earth . 2. by using dimensional analysis derive an expression for time period off a pendulum.

1) We have

? = 1°54' = 114' = 114 × 60" × 4.85 × 10^-6 rad = 3.32 × 10^-2 rad

 

The distance D of star from earth is D = d/?

Here, d is diameter of earth = 1.276 × 10⁷ m

 

Thus, we have

 

 

2) Let us say that time period depends on l, g and m as

 

T = k l^x g^y m^z

 

Consider dimensions of both sides of above equation

 

k is not found by dimensions. We have, K = 2 ?