Find out speed to the earth relative to sun assuming earth to rotate in a circular orbit around sun. Given: speed of light = 300 Mm/sec time taken by light to reach earth = 8 minutes
Lets calculate radius(r) of orbit in which earth rotates around sun, r = vt = (300*10^6)*8*60 = 144*10^9 metres Circumference of orbit = 2*3.14*r = (904.32)*10^9 m Time taken by earth to complete one rotation around sun = (365days)*(24hrs/day)*(3600seconds/hr) = 31.536 Msec Speed = circumference/time = 28675 m/sec
A Carnot's engine whose low temperature reservoir is at 27 °C has an efficiency of 40%. What should be the temperature of high temperature reservoir? What should be the temperature of the latter if the efficiency is to be raised to 80%?
We know that n = (T1 - T2)/T1 or 0.4 = (T1 - T2)/T1 or 0.4T1 = T1 − 300 or 0.6T1 = 300 or T1 = 500K Again, 0.8 = (T1 - T2)/T1 T1 = 1500 K it needs to be raised by 1000K.
Determine whether function f defined by f(x) = 2(x^2) for x <= 1 and f(x) = 2 sqrt(x) for x > 1 is differentiable at x = 1.
Check continuity of f(x) as well as f'(x) at x = 1 for it to be differential at x = 1. f(1) LHS = 2 f(1) RHS = 2 Continuous f'(1) LHS = 4 f'(1) RHS = 1 Not continuous and hence not differentiable.