A rocket accelerates straight up by
ejecting gas downwards. In a small
time interval Δt, it ejects a gas of mass
Δm at a relative speed u. Calculate KE
of the entire system at t + Δt and t and
show that the device that ejects gas
does work = ((1/2))Δmu^2 in this time
interval (neglect gravity).
A particle of mass m strikes on ground
with angle of incidence 45°. If coefficient
of restitution, e = (1/(√2)) , find the velocity
after impact and angle of reflection.
Let n be a positive integer and p_1 , p_2 ,
..., p_n be n prime numbers all larger
than 5 such that 6 divides p_1 ^2 + p_2 ^2 + ... +
p_n ^2 . Prove that 6 divides n.
ΔH_f ^o of N_2 O is 82 kJ/mol and bond
energy for N_2 , N = N, O = O and N = O
bonds are 946, 418, 498 and 607 kJ/mol
respectively, then resonance energy of
N_2 O is
A train weighing 100 metric ton is
running on a level track with a uniform
speed of 72 km h^(−1) . If the frictional
resistance amounts to 0.5 kg per metric
ton, find the power of the engine.