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A particle of mass m moves along a curve...

A particle of mass m moves along a curve `y=x^2`. When particle has x-coordinate as `(1)/(2)` m and x-component of velocity as `4(m)/(s)`, then

A

the position coordinate of particle are `((1)/(2)`,`(1)/(4))`m

B

The velocity of particle will be along the line `4x-4y-1=0`.

C

the magnitude of velocity at that instant is `4sqrt2(m)/(s)`

D

The magnitude of velocity at that instant is `2sqrt2(m)/(s)`.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
On the curve `y=x^2` at `x=(1)/(2)impliesy=(1)/(4)`
Hence the coordinate `((1)/(2)`,`(1)/(4))`
Differentiation: `y=x^2`, `v_y=2xv_x`
`v_y=2((1)/(2))(4)=4(m)/(s)`
Which satisfies the line
`4x-4y-1=0` (tangent to the curve) and magnitude of velocity:
`|vecv|=sqrt(v_x^2+v_y^2)=4sqrt2` m/s
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