A chain have linear mass density as λ= ax, where x is the distance from the point of application of force. This chain is placed on smooth surface as shown. Select the INCORRECT statement(s) (A) Tension at the centre of the chain is F/2 (B) Tension at the centre of the chain is 3F/4 (C) Tension decreases linearly as we move B to A. (D) If surface is sufficiently rough to avoid sliping than tension will be same throughout and it is equal to F.
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Let the mass of the rope AB be m .
Acceleration of the rope = a =
m
F
Let the force be applied at the end A and the point at a distance x from point A be P .
Tension in the rope at a distance x from end A (at point P)
= Force required to move the remaining part with acceleration a
Linear mass density of the rod =
l
m
Mass of the remaing part i.e. part PB =
l
m
(l−x)
Force required to move the remaining part = mass*acceleration
=
l
m
(l−x)
m
F
Therefore , tension in the rope at a distance x from the
end at which the force is applied is F(
l
l−x
Explanation:
hope it helps i couldnt type perfectly but you will understand
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