the corect relation b/w V1 & V2

a)V2=V1
b)V2=V1sin?
c)2V2sin?= V1
d)V2(1+sin?)=V1

Question

the corect relation b/w V1 & V2 a)V2=V1 b)V2=V1sin? c)2V2sin?= V1 d)V2(1+sin?)=V1

Pratham Ashish · Answer

hi,

at any time ,

let the length of string between the wedge & pully(which is stationary ) = x2

length of string between the block & pully (to which it is hanged ) = x1

length of string between the both pullys = x2/ cos(90-θ) = x2 / sinθ

since the length of strig would be const. so the sum of upper mentioned lenght would be const.

x1 + x2 + x2/ sinθ = const.

d/dt x1 + d/dt x2 + d/dt ( x2/ sinθ ) = 0

v1 - v2 - v2 /sin θ - x2 cosθ /sin^θ (d/dt θ) =0 .............(1)

let the height of the wedge be l,then

tan (90 -θ) = l / x2

x2 cot θ = l

cotθ d/dt x2 + x2 d/dt cot θ = 0

-cotθ v2 - x2 cosec^2 θ (d/dt θ) =0

cosθ sinθ v2 + x2 (d/dt θ) = 0

(d/dt θ) = - cosθ sinθ v2 /x2 ..............put in eq . (1)

v1 - v2 - v2 /sin θ - x2 cosθ /sin^θ (d/dt θ) =0

v1 - v2 - v2 /sin θ + x2 cosθ /sin^θ cosθ sinθ v2 /x2 =0

v1 - v2 - v2 /sin θ + v2 cos^θ / sinθ =0

v1- v2 - v2 /sinθ( 1 - cos^2θ ) = 0

v1 -v2 - v2 sinθ =0

v1 = v2 (1 + sinθ ) (d )

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