A particle of mass 1 kg moves with a constant speed v = 1 m / s along the curve A CB in vertical plane whose equation is y = 0.5 cos ℓ 2 π x , where x and y are in metre and ℓ = 1 m . The normal rea

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A particle of mass 1 kg moves with a constant speed $v = 1 m / s$ along the curve $A CB$ in vertical plane whose equation is $y = 0.5 cos \frac{2 π x}{ℓ}$ , where $x$ and $y$ are in metre and $ℓ = 1 m$ . The normal reaction on particle at lowest point $B$ is $(5 n) N$ . (take $π^{2} = 10$ and $g = 10 m / s^{2}$ ). The value of $n$ is

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As, dx dy ​ = − 0.5 × ℓ 2 π ​ sin ℓ 2 π ⋅ x ​ = 0 at B ​ ⇒ d x 2 d 2 y ​ = − 0.5 × ℓ 2 4 π 2 ​ cos ℓ 2 π x ​ = 2 π 2 at B ​ ⇒ R = ​ d x d 2 y ​ ​ [ 1 + ( d x d y ​ ) 2 ] 3/2 ​ ​ At point B , N − mg = ma r ​ = 2 π 2 m ​ N = 2 π 2 m + m g = m g ( g 2 π 2 ​ + 1 ) ​ = m g × 3 = 30 N = 5 n ​

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