Answer:
The number of revolutions turned by the centrifuge is 8250 revolutions.
Explanation:
Given;
number of revolution per minutes, ω = 15000 rpm
time of motion, t = 330 s = 5.5 minutes
The number of revolutions turned by the centrifuge is given by;
Therefore, the number of revolutions turned by the centrifuge is 8250 revolutions.
Given:
The masses of the balls, m₁=1 kg
m₂=2 kg
The height of 1 kg ball, h₁=6 m
The height of 2 kg ball, h₂=3 m
To find:
Which of the given statements are true?
Explanation:
From the law of conservation of energy, the energy can neither be created nor be destroyed. As the air resistance is negligible, the initial potential energy of the balls will be equal to their kinetic energy when they reach the ground.
Thus, the kinetic energy of the balls when they reach the ground is given by,
Where m is the mass of the balls, h is their respective height, and g is the acceleration due to gravity.
Thus the kinetic energy of mass m₁ is,
The kinetic energy of mass m₂ is,
The velocities of the balls will be given by the equation of kinetic energy.
Thus,
Where v is the respective velocities of the balls when they reach the ground.
On rearranging the above equation, the velocities will be given by,
On substituting the known values, the velocity of the mass m₁ is
The velocity of the mass m₂ is,
Thus the balls will have the same kinetic energies when they reach the ground. But the 1 kg ball will have a greater velocity than the 2-kg ball.
The time interval the ball takes is dependent on the height only and not on the mass. Thus the balls will not reach the ground at the same time.
Final answer:
Thus the correct answer is options are option B and option D.
Answer:
The potential energy is
Explanation:
Given that,
Force
We need to calculate the potential energy
Using formula of work done
Put the value of F
On integration
...(I)
U = 0, x = 0 so C = 0
Put the value of c and α in equation (I)
Hence, The potential energy is