C.
Newton’s Second Law is F=ma (force is equal to the mass multiplied by acceleration), however, the equation can be rearranged to isolate and calculate mass from force over acceleration. Therefore, m=F/a
Answer:

Explanation:
Consider two particles are initially at rest.
Therefore,
the kinetic energy of the particles is zero.
That initial K.E. = 0
The relative velocity with which both the particles are approaching each other is Δv and their reduced masses are

now, since both the masses have mass m
therefore,

= m/2
The final K.E. of the particles is

Distance between two particles is d and the gravitational potential energy between them is given by

By law of conservation of energy we have

Now plugging the values we get



This the required relation between G,m and d
Answer:
a) t=24s
b) number of oscillations= 11
Explanation:
In case of a damped simple harmonic oscillator the equation of motion is
m(d²x/dt²)+b(dx/dt)+kx=0
Therefore on solving the above differential equation we get,
x(t)=A₀
where A(t)=A₀
A₀ is the amplitude at t=0 and
is the angular frequency of damped SHM, which is given by,

Now coming to the problem,
Given: m=1.2 kg
k=9.8 N/m
b=210 g/s= 0.21 kg/s
A₀=13 cm
a) A(t)=A₀/8
⇒A₀
=A₀/8
⇒
applying logarithm on both sides
⇒
⇒
substituting the values

b) 

, where
is time period of damped SHM
⇒
let
be number of oscillations made
then, 
⇒
Answer:
The answer is 10.857mJ
Explanation:
The energy stored in this solenoid is given by the below mentioned equation,

where L the inductance of this solenoid is given by the below mentioned equation,

Plugging this into the energy equation you obtain the equation for the total energy stored in the magnetic field of the solenoid, given by,

where
is the permeability of free space which equals to
. Plugging all the quantities into the above equation from the data in the question after converting to standard units. of meters instead of centimeters, we get for the energy stored in the coil,
