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, 
⇒
A wheel and axle and an inclined plane.
Answer:
Explanation:
Given
charge on alpha particle=+2e
mass of alpha particle=
kg
Charge on gold nucleus=+79e
Velocity at r=1m is 
Using Energy conservation
Kinetic energy of particle will be converting to Potential energy as it approaches to nucleus
therefore


![\frac{1}{2}\left ( 6.64\times 10^{-27}\right )\left ( 1.9\times 10^{7}^2\right )=\frac{9\times 10^9\times 158\times \left ( 1.6\times 10^{-19}\right )}{y}\left [\frac{1}{r_0}-\frac{1}{1}\right ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cleft%20%28%206.64%5Ctimes%2010%5E%7B-27%7D%5Cright%20%29%5Cleft%20%28%201.9%5Ctimes%2010%5E%7B7%7D%5E2%5Cright%20%29%3D%5Cfrac%7B9%5Ctimes%2010%5E9%5Ctimes%20158%5Ctimes%20%5Cleft%20%28%201.6%5Ctimes%2010%5E%7B-19%7D%5Cright%20%29%7D%7By%7D%5Cleft%20%5B%5Cfrac%7B1%7D%7Br_0%7D-%5Cfrac%7B1%7D%7B1%7D%5Cright%20%5D)
on solving we get


ANSWER: Friction is a force that opposes motion. When two objects are in contact, friction is acts in a direction opposite to the motion of the object.
EXPLANATION: HOPE THIS HELPS.