The Potential energy stored in the system is 1 J
<u>Explanation:</u>
Given-
Mass, m = 4 kg
Spring constant, k = 800 N/m
Distance, x = 5cm = 0.05m
Potential energy, U = ?
We know,
Change in potential energy is equal to the work done.
So,

By plugging in the values we get,

Therefore, Potential energy stored in the system is 1 J
Auroras are frequently seen : B. After solar flares
The Aurora is created by an ongoing influx of particles into the Earth's existing magnetic field,
This particles originated from the Sun as part of Solar wind
hope this helps
Answer:
<u>For M84:</u>
M = 590.7 * 10³⁶ kg
<u>For M87:</u>
M = 2307.46 * 10³⁶ kg
Explanation:
1 parsec, pc = 3.08 * 10¹⁶ m
The equation of the orbit speed can be used to calculate the doppler velocity:

making m the subject of the formula in the equation above to calculate the mass of the black hole:
.............(1)
<u>For M84:</u>
r = 8 pc = 8 * 3.08 * 10¹⁶
r = 24.64 * 10¹⁶ m
v = 400 km/s = 4 * 10⁵ m/s
G = 6.674 * 10⁻¹¹ m³/kgs²
Substituting these values into equation (1)

M = 590.7 * 10³⁶ kg
<u>For M87:</u>
r = 20 pc = 20 * 3.08 * 10¹⁶
r = 61.6* 10¹⁶ m
v = 500 km/s = 5 * 10⁵ m/s
G = 6.674 * 10⁻¹¹ m³/kgs²
Substituting these values into equation (1)

M = 2307.46 * 10³⁶ kg
The mass of the black hole in the galaxies is measured using the doppler shift.
The assumption made is that the intrinsic velocity dispersion is needed to match the line widths that are observed.
Answer:
Explanation:
Given,
- Work done by the rope 900 m/s.
- Angle of inclination of the slope =

- Initial speed of the skier = v = 1.0 m/s
- Length of the inclined surface = d = 8.0 m
part (a)
The rope is doing the work against the gravity on the skier to uplift up to the inclined surface. Therefore the work done by the rope is equal to the work done on the skier due to the gravity

In both cases the height attained by the skier is equal. and the work done by gravity does not depend upon the speed of the skier.
part (b)
- Initial speed of the skier = v = 1.0 m/s.
Rate of the work done by the rope is power of the rope.

Part (c)
- Initial speed of the skier = v = 2.0 m/s.
Rate of the work done by the rope is power of the rope.

Answer:
4A
Explanation:
According to ohm's law;
E = IRt where;
E is the source voltage = 24volts
I is the total current flowing in the circuit = ?
Rt is the total effective resistance in the circuit.
To find Rt, we will resolve the resistors in parallel first.
Since 6ohms and 12ohms resistors are in parallel, their effective resistance will give;
1/R = 1/6+1/12
1/R= 2+1/12
1/R = 3/12
3R = 12
R = 4ohms.
This resistor will now be in series with the 2.0ohms resistor to finally have;
Rt = 4+2
Rt = 6ohms
From the ohms law formula;
I = E/Rt
I = 24/6
I = 4Amperes
The total current in the circuit is 4A
This same currents will flow in the 2ohms resistor since same current flows in a series connected resistors.