Answer:
If the frequency of the motion of a simple harmonic oscillator is doubled , then maximum speed of the oscillator changes by the factor 2
Explanation:
We know that in a simple harmonic oscillator the maximum speed is given by
= 
Here A is amplitude which is constant , so from above equation we see that maximum speed is directly proportional to
of the oscillation .
Since 
= 2
Where
is the maximum speed when frequency is doubled .
Answer:
(a) r = 1.062·R
= 
(b) r = 
(c) Zero
Explanation:
Here we have escape velocity v
given by
and the maximum height given by

Therefore, when the initial speed is 0.241v
we have
v =
so that;
v² =
v² = 
is then

Which gives
or
r = 1.062·R
(b) Here we have

Therefore we put
in the maximum height equation to get

From which we get
r = 1.32·R
(c) The we have the least initial mechanical energy, ME given by
ME = KE - PE
Where the KE = PE required to leave the earth we have
ME = KE - KE = 0
The least initial mechanical energy to leave the earth is zero.
Answer:
1.045 m from 120 kg
Explanation:
m1 = 120 kg
m2 = 420 kg
m = 51 kg
d = 3 m
Let m is placed at a distance y from 120 kg so that the net force on 51 kg is zero.
By use of the gravitational force
Force on m due to m1 is equal to the force on m due to m2.



3 - y = 1.87 y
3 = 2.87 y
y = 1.045 m
Thus, the net force on 51 kg is zero if it is placed at a distance of 1.045 m from 120 kg.
Answer:
Before start of slide velocity will be 14.81 m/sec
Explanation:
We have given coefficient of static friction 
Angle of inclination is equal to 


Radius is given r = 28 m
Acceleration due to gravity 
We know that 



So before start of slide velocity will be 14.81 m/sec
The tree might get swept away by the current and it will disappear when it catches on something