Answer:
4
Explanation:
Given that
Track is friction less
As we know that ,the velocity of the particle only depends on the height difference and does not depends on the path is incline or curve .
The final speed(v) of the roller at the bottom given as
From energy conservation
[tex]mgh=\dfrac{1}{2}mv^2[/tex]
[tex]v=\sqrt{2gh}[/tex]
If we want to twice the speed ,it means that
v'= 2v
lets take height difference is h'
[tex]v'=\sqrt{2gh'}[/tex]
[tex]2v=\sqrt{2gh'}[/tex]
[tex]2\sqrt{2gh}=\sqrt{2gh'}[/tex]
4 x 2 g h = 2 g h'
So
h'=4 h
The height have to increase by 4 factor.
The height of the track will be increased by four times h'=4h
It is given that
The track is frictionless
As we know, the velocity of the particle only depends on the height difference
From the energy conservation, the final speed(v) of the roller at the bottom is given as
[tex]PE= KE[/tex]
[tex]mgh=\dfrac{1}{2}mv^2[/tex]
[tex]v=\sqrt{2gh}[/tex]
If the speed has to be twice
[tex]v'=2v[/tex]
Now at this speed light will be [tex]h'[/tex]
So now
[tex]v'=\sqrt{2gh'}[/tex]
[tex]2v=\sqrt{2gh'}[/tex]
[tex]2\sqrt{2gh} =\sqrt{2gh'}[/tex]
[tex]4\times 2gh=2gh'[/tex]
[tex]h'=4h[/tex]
Thus the height of the track will be increased by four times h'=4h
To know more about the conservation of energy follow
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