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A particle is placed at the point A of a...

A particle is placed at the point A of a frictionless track ABC as shown in figure. It is pushed slightly towards right. Find its speed when it reches the point B. Take `g=10 m/s^2`.

Text Solution

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Let us take the gravitatioN/Al potential energy to be zero t the horizontal surface shown in the ure. The potential energies of the particle at A and B are
`U_A=Mg(1m)`
and `U_B=Mg(0.5)m`
The kinetic energy at the point A is zero. As the track is frictionless, no energy is lost. The normal force o the particle does no work. Applying the principle off conservation of energy
`U_A+K_A=U_B+K_K`
or, `Mg(1m)=Mg(0.5m)+1/2Mv_B^2`
or, `1/2v_B^2=g(1m-0.5m)`
`=(10 m/s^2)xx0.5m`
`=5m^2/s^2`
or `v_B=sqrt10 m/s`.
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