Mechanics | Relativity Answers

a) Consider a simple pendulum of mass m mounted inside a railroad car that is accelerating
to the right with constant acceleration a. Analyse this problem in the non inertial frame
of reference to find the angle alfa(F) with the vertical direction at which the pendulum will
remain at rest relative to the moving car.
b) On Jupiter a day lasts for 9.9 earth hours and the circumference at the equator is
448600 km. If the measured value of gravitational acceleration at the equator is
24.6ms^-2, what is the true gravitational acceleration and the centrifugal
acceleration.

a) A particle of mass 4.0 kg, initially moving with a velocity of 5.0m/s collides elastically
with a particle of mass 6.0 kg, initially moving with a velocity of -8.0m/s.What are
the velocities of the two particles before and after the collision in the centre of mass
frame of reference? What are the velocities of the two particles after the collision in the
laboratory frame?
b) A 30.0 kg girl stands at the rim of a merry-go-round that has a moment of inertia of
500kgm^2 and a radius of 3.00 m. The merry-go-round is initially at rest. The woman
then starts walking around the rim clockwise at a constant speed of 2.0m/s .
i) In what direction and with what angular speed does the merry-go-round rotate?
ii) How much work does the girl do to set herself and the merry-go-round into motion?

a) An L-shaped object of uniform density is hung over a nail so that it is free to rotate.
Determine the angle that the long side of the object makes with the vertical. The long
side of the L-shaped object is given to be twice as long as the short side.
b) A solid cylinder rolls up an inclined plane without slipping. If the incline makes an angle
of 30º to the horizontal and the coefficient of static friction is μs = 0.40, find its
acceleration. Also determine the angle of the inclined plane at which the object will start
to slip.

a) The distance between the oxygen molecule and each of the hydrogen atoms in a water
(H2O) molecule is 0.96 Å and the angle between the two oxygen-hydrogen bonds is
105°. Treating the atoms as particles, find the centre of mass of the system.
b) A stationary ball, with a mass of 0.2 kg, is struck by an identical ball moving at
4.0 m/s. After the collision, the second ball moves 60° to the left of its original
direction. The stationary ball moves 30° to the right of the moving ball’s original
direction. What is the velocity of each ball after the collision?

A skier is gliding along at 2.0m/s on horizontal, frictionless snow. He suddenly starts down a 15∘ incline. His speed at the bottom is 12m/s .

Part A
What is the length of the incline?

Part B
How long does it take him to reach the bottom?

four thin uniform rods of mass m and length are joined to form a square. what will be the moment of inertia about an axis along its one diagonal?

a man swim across a river with speed of Vm perpendiculuar to the flow of direction of river .if water flows with the speed of Vw ,then what is direction of man to cross river ...................how we place theta in this question.....how we know we hv to place theta either in x or y diection ......with resultant velocity pls tell me

A steel ball of vol. 1 cm3 is recat in a hollow sphere to float in water.what should be the minimum volume of this sphere.

what is the cross product A >< B under mirror reflection

Take the mass of the Earth to be 5.98 × 10^24 kg. If the Earth’s gravitational force causes a falling 65 kg student to accelerate downward at 9.8m/s^2, determine the upward acceleration of the Earth during the students fall.