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## Equilibrium – Numerical Problem

SOLID HEMISPHERE OF RADII R EACH, are placed in contact with each other with each other with their flat faces on a rough horizontal surface. A sphere of mass m and radius R is placed symmetrically on top of them. The normal reaction between the top sphere and any hemisphere assuming the system to be in state equilibrium is

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## Time Dilation problem – Special Relativity

With what speed will a clock have to be moving in order to run at a rate that is one half the rate of a clock at rest?

Posted by Mona

Answer:

Using the formula for Relativistic Time (according to Special Theory of Relativity)

√[1 – (v²/c²)] = ½ → v² = (3/4)c²

v = [√3/2]*c = .866c

## Question from Special Relativity

A spacecraft starts from earth moving at constant speed to planet A which is 20 light-hour away from Earth.

It takes 25 hour (according to an earth observer) for a spacecraft to reach this planet. Assuming that clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft frame for this one-way journey with the time elapsed as measured by an earth-based clock?

Posted by Mona

## Angle between acceleration and velocity in projectile motion

What is the angle between the directions of acceleration and velocity at the highest point of projectile?

Answer:

At the highest point of a projectile, the vertical component of velocity is zero and the velocity is entirely **horizontal.** The direction of acceleration (due to gravity) is vertically downwards throughout the motion of the projectile.

Therefore, **the angle between the direction of acceleration and velocity at the highest point of a projectile is 90 °**

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## Displacement – A Numerical Problem

A fly is sitting in the middle of a wall of a cubic room of side ’a’.If it flies and sit to one of opposite corner of the wall. Find its displacement?

**Answer:**

**A to B**in the diagram) the displacement is “

**a**“

**A to C**in the diagram) the displacement is “

**√2 a**“

**A to H**in the diagram) the displacement is “

**√3 a**“

## A problem from Dynamics

The coefficient of kinetic friction between the 2.00-kg and 3.00-kg blocks

is 0.300. The horizontal surface and the pulleys are frictionless, and the masses are released from rest.

a) Draw a free-body diagram for each block.

b) Determine the acceleration of each block.

c) Find the tension in the strings.

## Physics Problem Link

Try to solve this Problem

Kinematics Problem

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