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The equation of a tangent to the para...

The equation of a tangent to the parabola `y^2=""8x""i s""y""=""x""+""2` . The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is (1) `(-1,""1)` (2) `(0,""2)` (3) `(2,""4)` (4) `(-2,""0)`

A

`(5h)/(8)`

B

`(3h)/(5)`

C

`(5h)/(7)`

D

`(7h)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
C
Total kinetic energy of a body which is rolling without slipping is given by `K_("total")=K_("rot")+K_("trans")`
`I=(2)/(5)MR^(2)and v=Romega` (along the diameter)
Where, R is radius of spherical ball,
So, `K_("total")=(1)/(2)((2)/(5)mR^(2))omega^(2)+(1)/(2)mR^(2)omega^(2)`
`=(7)/(10)mR^(2)omega^(2),K=(7)/(10)mv^(2)`
Potential energy = Kinetic energy
`mgh=(7)/(10)mv^(2)rArrv^(2)=(10)/(7)gh`....(i)
For vertical projection
`v^(2)=u^(2)+2gh'rArr(10)/(7)gh=0+2gh'rArrh'=(5)/(7)h`.
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