Mechanics | Relativity Answers

A 40g marble with a 5mm radius is rolling at 10 revolutions per second, towards a spring attached to a wall. The spring is initially at its equilibrium length, and has a spring constant of 12 N/m. The marble hits the spring, and then eventually comes momentarily to rest. How far has the spring recoiled when the marble is at rest? 

You are in charge of a project that requires having a communications satellite orbiting the earth as fast as possible. A Canadian corporation has said that the best they can do is to provide a 50 kg satellite that will orbit the earth is 5 * 10^3 s. An American company said that because of advance lightweight materials they can build the same satellite with a mass of 12.5 kg and have it orbit at 7.94 * 10^3 m/s. which satellite will you order? Show calculation to justify your choice.

What is the total energy of an electron when its momentum is 10 times its it is multiplied by the light velocity (rest mass of electron equals to 9×10^-31 kg)

The half life of a particle in the laboratory is 4×10^-8 sec, when its speed is 0.8c . with half life will be measured in the laboratory if the speed of the particle is reduces 0.6c
1)2×10^-8 sec
2)3××10^-8 sec
3)1×10^-8 sec
4)0.75×10^-8 sec

Two particle comes towards each other with a speed 0.8c with respect to the laboratory their relative speed is

A nuclear particle was observed to break into two fragments which moved in opposite direction the velocity of each fragment was found to be 2.5×10^8 m/s. relative to the laboratory the velocity of the one fragment relative to other is

The lifetime of π-mesons is 2.5×10^-8 and their speed is 2.7×10^8m/s the distance travelled by π-mesons as seen by the observer on the earth during their lifetime is

General calculation of mean of random walk

Three balls (mA=15kg, mB=12kg, mC=35kg) are places at the corners of a right angle triangle as shown. Ball A is directly north of ball B and ball C is directly east of ball B. Calculate the net force on ball B due to the presence of the other two balls. Write out all formulas, free body diagrams and calculations to get full marks

the case of pure rolling of a disc on rough horizontal surface the ratio of speed at top most point and the centre of mass is
1)2:1
2)1:2
3)1:1
4)√2:1