Physics, 12.08.2019 16:20 qwerty9951

Two spheres having masses m and 2m and radii r and 3r, respectively, are released from rest when the distance between their centers is 12r. how fast will each sphere be moving when they collide? assume that the two spheres interact only with each other.

Answers: 3

Show answers

Answers

Answer from: michaelmorrison37

$v_2 = \sqrt{\frac{GM}{3R}}$

$v_1 = 2\sqrt{\frac{GM}{3R}}$

Explanation:

As we know by energy conservation that change in gravitational potential energy of the system = change in kinetic energy of the two ball

So here we can say

$-\frac{GM(2M)}{12R} + 0 = -\frac{GM(2M)}{4R} + \frac{1}{2}Mv_1^2 + \frac{1}{2}(2M)v_2^2$

Also since there is no external force on the system of two masses so here total momentum of the two balls will remains conserved

0 = Mv_1 + 2Mv_2

v_1 = -2v_2

now we have

$\frac{GM^2}{2R} - \frac{GM^2}{6R} = \frac{1}{2}M(-2v_2)^2 + \frac{1}{2}(2M)v_2^2$

$\frac{GM^2}{3R} = Mv_2^2$

$v_2 = \sqrt{\frac{GM}{3R}}$

$v_1 = 2\sqrt{\frac{GM}{3R}}$

Answer from: Quest

If there was no gravity then their would be no downword force on the football to have it return the the grownd, and if there was no friction (mainly air friction) then there would be no opposing force the stop the ball from moving through the air allowing the ball to travle ∞.

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Another question on Physics

Physics, 22.06.2019 06:00

An ideal gas is held in a container at constant volume. initially, its temperature is 5 degrees c and its pressure is 1.2 atm. what is its pressure when its temperature is 43 degrees c? answer in units of atm

Answers: 2

Answer

Physics, 22.06.2019 07:50

Determine the fraction of the magnitude of kinetic energy lost by a neutron (m1 = 1.01 u) when it collides head-on and elastically with a target particle at rest which is 21h (heavy hydrogen, m = 2.01 u).

Answers: 3

Answer

Physics, 22.06.2019 09:30

How would a small bar magnet be oriented when placed at position x?

Answers: 2

Answer

Physics, 22.06.2019 19:30

The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by a square well. imagine a proton conned in an innite square well of length 105 nm, a typical nuclear diameter. calculate the wavelength and energy associated with the photon that is emitted when the proton undergoes a transition from the rst excited state (n 2) to the ground state (n 1). in what region of the electromagnetic spectrum does this wavelength belong?

Answers: 1

Answer

You know the right answer?

Two spheres having masses m and 2m and radii r and 3r, respectively, are released from rest when the...

Questions