(a) The capacitance of the capacitor is:

and the voltage applied across its plates is

The relationship between the charge Q on each plate of the capacitor, the capacitance and the voltage is:

and re-arranging it we find the charge stored in the capacitor:

(b) The electrical potential energy stored in a capacitor is given by

where C is the capacitance and V is the voltage. The new voltage is

so the energy stored in the capacitor is
Answer:
The correct option is: B that is 1/2 K
Explanation:
Given:
Two carts of different masses, same force were applied for same duration of time.
Mass of the lighter cart = 
Mass of the heavier cart = 
We have to find the relationship between their kinetic energy:
Let the KE of cart having mass m be "K".
and KE of cart having mass m be "K1".
As it is given regarding Force and time so we have to bring in picture the concept of momentum Δp and find a relation with KE.
Numerical analysis.
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⇒ 
⇒ 
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⇒ 
Now,
Kinetic energies and their ratios in terms of momentum or impulse.
KE (K) of mass m.
⇒
...equation (i)
KE (K1) of mass 2m.
⇒ 
⇒
...equation (ii)
Lets divide K1 and K to find the relationship between the two carts's KE.
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⇒ 
⇒ 
⇒ 
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⇒ 
The kinetic energy of the heavy cart after the push compared to the kinetic energy of the light cart is 1/2 K.
Answer:

Explanation:
Let's use the decay equation.

Where:
- A is the activity at t time
- A₀ is the initial activity
- λ is the decay constant
We know that 
So we have:




Therefore, the half-life of the source is 6 hours.
I hope it helps you!
Answer:
Like charges repel each other; unlike charges attract. Thus, two negative charges repel one another, while a positive charge attracts a negative charge. The attraction or repulsion acts along the line between the two charges. The size of the force varies inversely as the square of the distance between the two charges.