You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Strength of Materials

Shear Force and Bending Moment

Two people we...

Question

Two people weighing W each are sitting on a plank of length L floating on water at L/4 from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is

\frac{W L}{8}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{W L}{16}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{W L}{32}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Zero

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D Zero

Plank is floating so net upward force will be equal to 2W and it will act as a UDL on the plank. So load intensity of

$U D L = \frac{2 W}{L}$

Bending moment at the centre

$M = \frac{1}{2} (\frac{2 W}{L}) {(\frac{L}{2})}^{2} - W \times \frac{L}{4}$

$= \frac{1}{2} \times \frac{2 W}{L} . \frac{L^{2}}{4} - \frac{W L}{4}$

$= \frac{W L}{4} - \frac{W L}{4} = 0$

Suggest Corrections

Similar questions

Q. A body of mass

m

stands on end of a wooden plank of length

L

and mass

M

. The plank is floating on water. If the body walks from one end of the plank to the other end at a constant speed, the resulting displacement of the plank is given by :

Q. The plank of a seesaw is

8 m

long and is supported at the centre. Neil, who weighs

80 kgf

sits at a distance of

3 m

from the fulcrum. John sits

4 m

from the fulcrum to balance the plank. What is John's weight?

Q. A uniform wooden plank

5 m

long and weighting

40 k g

is resting on two supports

0.5 m

from each end. A boy weighting

45 k g

stands

1.5 m

from one end of the wooden plank. Find the reactions at the supports.

Q. A wooden uniform plank of length 20 m and weight 500 N is placed horizontally, supported on the two ends. A dog of weight 625 N is walking on the plank towards the right (as shown in the given figure). When the dog reaches point P, the left end of the plank is about to lift up. What is the distance of point P from the Centre of gravity of the plank? ___

A plank of a See-saw is 8m long and is supported at the centre. Rahul, who weighs 80 Kgf sits at a distance of 3 m from the fulcrum. Manish sits 4m from the fulcrum to balance the plank. What is Manish's weight

Join BYJU'S Learning Program

Two people weighing W each are sitting on a plank of length L floating on water at L/4 from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is

The correct option is D Zero Plank is floating so net upward force will be equal to 2W and it will act as a UDL on the plank. So load intensity of UDL=2WL Bending moment at the centre M=12(2WL)(L2)2−W×L4 =12×2WL.L24−WL4 =WL4−WL4=0