The tube shown is of non-uniform crossection the cross-section area at A is half of the cross-section area at B, C and D a liquid is flowing through in steady state. The liquid exerts on the tube Statement:I- A net force towards right.
Statement:II-A net force towards left
statement:III-A net force in some oblique direction
Statement:IV-Zero net force
Statement V: A net clockwise torque.
Statement:VI-A net counter-clockwise torque.
(A). Only statement I and V are correct
(B). Only statement II and VI are correct
(C). Only statement IV and VI are correct
(D). Only statement III and VI are correct.

Answer

A

Explanation

The force has been exerted by liquid on the tube due to change I momentum at the corners i.e., when liquid is taking turn from A to B and from B to C. As cross-section area at A is half of that of B and C, so velocity liquid flow at B and C is half to that of velocity at A. let velocity of flow of liquid at A ve v and cross section area at A be S, The velocity of flow of liquid at B and C would be `(v)/(2)` [from continuity equation] and cross section area at B and C would be 2S.
Due to flow of liquid, it is exerting a force per unit time of `rhoSv^(2)` on the tube, where `rho` is the density of liquid, S is cross section area and v is velocity of flow of liquid. the force exerted by liquid on tube is shown in the figure which clearly shows that a net force is acting on tube due to flowing liquid towards right and a clockwise torque.