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

Byju's Answer

Standard VIII

Physics

Floating and Sinking

Two cylinders...

Question

Two cylinders of same cross-section and length $L$ but made of two material of densities $d_{1}$ and $d_{2}$ are cemented together to form a cylinder of length $2 L$ . The combination floats in a liquid of density $d$ with a length $L / 2$ above the surface of the liquid. If $d_{1} > d_{2}$ then

d_{1} > \frac{3}{4} d

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

\frac{d}{2} > d_{1}

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

\frac{d}{4} > d_{1}

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

d < d_{1}

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

Open in App

Solution

The correct option is A $d_{1} > \frac{3}{4} d$
According to law of floatation, a body floats if weight of the body is equal to the weight of water displaced. So we have
$(d_{1} + d_{2}) L A g = \frac{3}{2} L A d g$ since $(2 L - \frac{L}{2}) = \frac{3 L}{2}$ length of cylinder is inside liquid.
$(d_{1} + d_{2}) = \frac{3}{2} d \Rightarrow d_{2} = \frac{3}{2} d - d_{1}$
Since $d_{1} > d_{2}$ , we have
$d_{1} > \frac{3}{2} d - d_{1} \Rightarrow 2 d_{1} > \frac{3}{2} d \Rightarrow d_{1} > \frac{3}{4} d$

Suggest Corrections

Similar questions

Q. Two cylinders of same cross-section and length

L

but made of two different materials of densities

d_{1}

and

d_{2}

are cemented together to form a cylinder of length

2 L

. The combination floats in a liquid of density

d

with a length

\frac{L}{2}

above the surface of the liquid. If

d_{1} < d_{2}

then

Two cylinders of same cross section area and length L but made of two material of densities $d_{1}$ and $d_{2}$ are connected together to form a cylinder of length 2L. The combination floats in a liquid of density d with a length $\frac{L}{2}$ above the surface of the liquid. If $d_{1} > d_{2}$ then

Q. Two cylinders of same cross-section and length

L

but made of two different materials of densities

d_{1}

and

d_{2}

are cemented together to form a cylinder of length

2 L

. The combination floats in a liquid of density

d

with a length

\frac{L}{2}

above the surface of the liquid. If

d_{1} < d_{2}

then

A body of density d and volume V floats with volume $V_{1}$ of it immersed in a liquid of density $d_{1}$ and rest of the volume $V_{2}$ immersed in another liquid of density $d_{2}$ (< $d_{1}$ ) then $V_{1}$ is

Q. In the arrangement as shown, A and B are two cylinders each of length L and density

d_{1}

and

d_{2} (d_{1} < d_{2})

, respectively. They are joined together and submerged in the liquid of density d with length L/2 of A outside the liquid. If the difference in densities of two cylinders is equal to density of the liquid, find

d_{1}

Join BYJU'S Learning Program

Two cylinders of same cross-section and length L but made of two material of densities d1 and d2 are cemented together to form a cylinder of length 2L. The combination floats in a liquid of density d with a length L/2 above the surface of the liquid. If d1>d2 then

Two cylinders of same cross-section and length $L$ but made of two material of densities $d_{1}$ and $d_{2}$ are cemented together to form a cylinder of length $2 L$ . The combination floats in a liquid of density $d$ with a length $L / 2$ above the surface of the liquid. If $d_{1} > d_{2}$ then