Mechanics | Relativity Answers

A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2M. The block and the man are in rest on the wedge. The man pulls the rope. Pulley is massless and frictionless. What is the displacement of the wedge when the block meets the pulley. ( man does not leave his position during the pull )

For a damped harmonic oscillator, the equation of motion is
( / ) ( / ) 0 2 2
m d x dt + g dx dt + kx =
with m = 0.50 kg, g = 0.70 kgs−1 and k = 70 Nm−1. Calculate (i) the period of motion,
(ii) number of oscillations in which its amplitude will become half of its initial value,
(iii) the number of oscillations in which its mechanical energy will drop to half of its
initial value, (iv) its relaxation time, and (v) quality factor

Q. 1 An automobile travelling at 80 km hr 1 has tyres of radius 80 cm. On applying brakes, the car is brought to a stop in 30 complete turns of the tyres. What is the magnitude of the angular acceleration of the wheels? How far does the car move while the brakes are

applied?
Q. 2 The position vector of two particles of mass 4.0 kg and 2.0 kg are, respectively,




r


ˆ


ˆ


2 ˆ


r


ˆ


2


ˆ


ˆ












r1 = 3t i


+ t j + 2t


k


and r2 = 3 i + (t





1)j + 4t k where t is in seconds and the position




in metres. Determine the position vector of the centre of mass of the system, the




velocity of the cm and the net force acting on the system.

An emf of 100 V is applied to a series RC circuit in which the resistance is 200 ohms & the capacitance is 10/10000 farad. Determine the charges q(t)=0. Also determine the current i(t).

A truck moving at a speed of 144km/hr passes a car moving at a speed of 72 km/hr .. If the truck sounds its horn at a frequency of 500Hz , what is the frequency of sound heard by the person the car?

The position vector of two particles of mass 4.0 kg and 2.0 kg are, respectively,
r i j kˆ 2
ˆ ˆ 3
2
1 = t + t + t
r
and r i ( )j kˆ 4
ˆ 1
ˆ 3
2
2 = + t − + t
r
where t is in seconds and the position
in metres. Determine the position vector of the centre of mass of the system, the
velocity of the cm and the net force acting on the system.

Define weightlessness and explain its conditions by using example.

What is artificial gravity how it is produced.If a space craft of length 20m enters in space then what should be its velocity to produce artificial gravity as earth.

An insect of mass 20g crawls from the centre to the outside edge of a rotating disc of mass 200g and radius 20cm. The disc was initially rotating at 22.0 rad/s. What is the change in the kinetic energy of the system?

Use the Frobenius method to obtain one solution of the following ODE:
4 yx ′′ + 2y′ + y = 0