Consider the earth as a uniform sphere of mass And Radius . Imagine a straight smooth tunnel made through the earth which connects any two points on its surface (The two points are not diametrically opposite). Determine the time that a particle would take to go from one end to the other through the tunnel. If Your answer is , then find the value of to the nearest integer.
Details And Assumptions:
Consider only gravitation force due to earth be acting on the particle during its motion along the tunnel.
Take acceleration due to gravity on surface of Earth =
Radius of Earth = .
This is an entry for the problem writing party.
A block of mass is gently attached to the spring and released at time , when the spring has its free length. During subsequent motion of the block, the displacement of the block with respect to time is considered. Find
Details and Assumptions
A mass is subjected to a force Initially the mass lies at the origin at rest. In the definition of force (given) refers to the -coordinate of the mass and t refers to the time elapsed.
Find the x - coordinate of the mass after a time of 4 seconds.
Assumptions
1) All the values are in SI units.
2) Take the mass = 1 kg, a = 1 N/s, b = 1 N/m
If the time period of SHM of rectangular block can be represented as
Find the value of .
Details and Assumptions:
Treat the pulley as a disc.
The block and pulley are oscillating in the same phase with the same frequency.
Pulley has sufficient friction for Pure Rolling and mass=m & strings are light and inextensible.
Gravity is present.
Zig-zag lines in fig represents spring of spring constant and as shown.
a is a square-free integer and the fraction is in simplest form.
A smooth wedge of mass and angle of inclination is attached to two springs of spring constant on the left, and on the right. The wedge rests on a smooth frictionless plane. Find the period of oscillation of the wedge in seconds.
Give your answer to 3 decimal places.
Details and Assumptions: