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Grade 11Mechanics

A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.

Simran Bhatia

12 Years agoGrade 11

4 Answers

Kevin Nash

12 Years ago

Sol. Let x → edge of ice block When it just leaves contact with the bottom of the glass. h→ height of water melted from ice W = U ⇒x3 * pice * g = x2 * h * pw * g Again, volume of water formed, from melting of ice is given by, 43 – x3 = π * r2 * h – x2h ( because amount of water = (πr2 – x2)h) ⇒43 – x3 = π * 32 * h – x2h Putting h = 0.9 x ⇒x = 2.26 cm

boss

10 Years ago

Thats exactly whats in the hcv pdf solution. We expect faculties to give their own solution. Who wil join such classes which have such faculties

Sanjeev Srivastava

7 Years ago

We can visualize the melting of ice in three stages.

Stage 1 : Ice = m Water = 0

Stage 2 : Ice = m-x Water = x (Ice still on surface)

Stage 3 : Ice = m-x' Water = x' (Ice floating on surface)

Now, In the question it is asked to find the edge length at time it just leaves the contact(last moment of stage 2). Therefore, we will study stage 2 rather than stage 3.

Follow the HCV Solution. I hope you understand it now. :)

(Volume dispersed by the block = x²h . density of water) = (Volume of the block at time t)

Ta

6 Years ago

Let volume of water melted be 64-x³(x is edge length of ice after being melted).

And volume of ice =x³

Now net volume =π*9*x(since radius =3cm )

Now,(64-x³)+x³=9πx

=>x=64/9π=2.26cm.

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