Yes, the volume of the cylinder will remain constant. As the radius decreases, the height will increase to make sure that the volume is kept the same.
We have been given a value of dr/dt and are required to find dh/dt
Because the volume is constant, we can plug it into the formula for the volume of the cylinder and rearrange it to make h the subject:
128 = πr²h
h = 128/πr²
Now we differentiate both sides:
dh/dr = -256/πr³
Applying the chain rule:
dh/dt = dh/dr x dr/dt
dh/dt = (-256/πr³) x -0.05
dh/dt = 64/5πr³; substituting the value of r
dh/dt = 64/5π(1.5)³
dh/dt = 1.21 in/sec
Option A looks like the best definition
Answer : The temperature when the water and pan reach thermal equilibrium short time later is, 
Explanation :
In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.
where,
= specific heat of aluminium = 
= specific heat of water = 
= mass of aluminum = 0.500 kg = 500 g
= mass of water = 0.250 kg = 250 g
= final temperature of mixture = ?
= initial temperature of aluminum = 
= initial temperature of water = 
Now put all the given values in the above formula, we get:
Therefore, the temperature when the water and pan reach thermal equilibrium short time later is,
Answer:
857.5 m
2.8583×10⁻⁶ seconds
Explanation:
Time taken by the sound of the thunder to reach the student = 2.5 s
Speed of sound in air is 343 m/s
Speed of light is 3×10⁸ m/s
Distance travelled by the sound = Time taken by the sound × Speed of sound in air
⇒Distance travelled by the sound = 2.5×343 = 857.5 m
⇒Distance travelled by the sound = 857.5 m
Time taken by light = Distance the light travelled / Speed of light
Time taken by light = 2.8583×10⁻⁶ seconds
Answer: A Bowling Ball
Explanation:
A body possess kinetic energy due to virtue of its motion. It depends on the mass of the body and the speed with which it is travelling.
K.E = 0.5 mv²
K.E. ∝ m
It is given that the marble, bowling ball, basketball and baseball all are rolling with the same speed. This means that the greatest energy would be possessed by the body having greatest mass.
On an average the mass of a marble is about 50 g, mass of a bowling ball is 750 g, mass of baseball is 150 g and mass of basketball is 600 g. Since the mass of a Bowling ball is the greatest, it would possess the greatest kinetic energy.
