Pls answer this question-
Four workers are sitting on the top four corners of a cubical room.These workers are trying to vertically lower a ceiling fan with the help of ropes. The workers are releasing the ropes with a constant speed v0 each and the ceiling fan is coming down vertically along a line passing through the body centre of the room.At the instant the ceiling fan is passing through the body centre of the room,its speed is
a)v0/31/2
b)v031/2
c)(v031/2)/2
d)2v0 /31/2
is the ans 'b'
please reply
your answer is absolutely correct.
could u pls explain how you did it.
b) is the right option!
Consider the upper diagonal of the cube. Let the lenght of a side of the cube be a. Therefore diagonal=a(2)1/2. Drop a perpendicular from the centre of the cube onto this diagonal. The lenght of this perpendicular is a/2. Distance of the pt. of intersection of the perpendicular with this diagonal from any vertice of the cube is a(2)-1/2.
Solution: Let at any pt. the lenght of the rope from the fan to the worker be x and the depth of the fan from the diagonal be h. From the pythagorean theorem we have x2 = h2 + a2/2.
Differentiating the above equation w.r.to .time we have 2xv0=2h(vreq). Hence (vreq) = (v0)(x/h). At bodycentre h=a/2 and x=[ a2/2 + a2/4 ]1/2= [(3)1/2(a)/2]. Hence: (vreq)= (v031/2)/2