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प्रश्न
A body starts slipping down an incline and moves half metre in half second. How long will it take to move the next half metre?
उत्तर
Let a be the acceleration of the body sliding down. 
From the above diagram:
R − mg cos θ = 0
⇒ R = mg cos θ (1)
and
ma + mg sin θ − μR = 0
`=> a = ("mg"(sintheta-mu costheta))/m="g"(sintheta-mu costheta)`
For the first half metre, u = 0, s = 0.5 m and t = 0.5 s.
According to the equation of motion,
v = u + at
= 0 + (0.5)4 = 2 m/s
`s=ut+1/2at^2`
`0.5=0+1/2a(0.5)^2`
⇒ a = 4 m/s2
For the next half metre, u = 2 m/s, a = 4 m/s2 and s = 0.5.
`=>0.5=2t+(1/2)4t^2`
⇒ 2t2 + 2t − 0.5 = 0
⇒ 4t2 + 4t − 1 = 0
`=>t=(-4+-sqrt(16+16)(2xx4)`
`=1.656/8=0.2027`
Therefore, the time taken to cover the next half metre is 0.21 s
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संबंधित प्रश्न
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The contact force exerted by a body A on another body B is equal to the normal force between the bodies We conclude that
(a) the surface must be frictionless
(b) the force of friction between the bodies is zero
(c) the magnitude of normal force equal that of friction
(d) the bodies may be rough but they don't slip on each other.
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