Classical Mechanics
# Conservation of Energy

$m = 5 \text{ kg }$ slides down from the top of a hemisphere of radius $R = 6 \text{ m }.$ The speed of the ball when it loses contact with the hemisphere can be expressed as $v = \sqrt{\frac{a}{b}} \text{ m/s},$ where $a$ and $b$ are coprime positive integers. Find the value of $a+b.$

A ball of massThe gravitational acceleration is $g= 10 \text{ m/s}^2.$

$m = 7 \text{ kg}$ falls towards the ground from a height of $H = 8000 \text{ km} .$ When the ball's height is $h = 3000 \text{ km} ,$ its speed can be expressed as $v = \sqrt{\frac{GM\times a}{b}} \text{ km/s},$ where $a$ and $b$ are coprime positive integers. If the air resistance is negligible, what is the value of $a+b?$

A ball of mass$G$ is gravitational constant and $M$ is the mass of the earth. The radius of the earth is $R = 6000 \text{ km} .$

$m = 5 \text{ kg }$ slides down from the top of a frictionless hemisphere of radius $R = 12 \text{ m} .$ At what height $h$ does the ball lose contact with the hemisphere?

A ball of massThe gravitational acceleration is $g= 10 \text{ m/s}^2.$

$m = 5 \text{ kg}$ falls down towards the ground from a height of $h = 3000 \text{ km}.$ The speed with which the ball strikes the ground is $v = \sqrt{\frac{GM\times{a}}{b}} \text{ km/s},$ where $a$ and $b$ are coprime positive integers. If the air resistance is negligible, what is the value of $a+b?$

A ball of mass$G$ is the gravitational constant and $M$ is the mass of the earth. The radius of the earth is $R = 6000 \text{ km} .$