Question

The mass of a solid iron cube of side 3 cm is to be determined by using a spring balance. If the density of iron is about 8.5 g / cm³, what should be the least count of the best suited spring balance to determine the weight of solid? Explain in detail.

Points : 20 ☺

Answer 1

volume of cube =(edge length)^3 =(3cm)^3 =27cm^3

density =8.5g/cm^3
mass = vol x density
=8.5 x 27 =229.5 g
hence,
range of mass is zero to 230
hence, spring slide between zero to 230

we see in the picture of spring balance ,
least count for range zero to 200g is 2N
it means
least count for range 0 to 230 is 2.295 N

Answer 2

I am not sure, but answer could be:  (in order decreasing preference)

          Range 0 to 250 gms (any >230 gms) ,  L.C. = 0.5 gms
          Range 0 to 250 gms (>230 gms), L.C. = 1 gm
          Range 0 to 250 gms (>230 gms),  L.C.= 2.5 gms
          Range 0 to 500 gms (>230 gms).  L.C. = 5 gms

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Iron cube : volume is approximately = 3³ = 27 cm³
                  density approx : 8.5 gm/cm³
                  approx mass = 229.5 gms

So we need a spring balance that has a (capacity) range from 0 to 230 gms or, 0 to 2.295 N  at least.

The spring balance in the picture has a range of 0 to 200 gms with a least count of 2 gms.  (or 0 to 2.0 N with a least count of 0.02N).

We could choose a spring balance with a range of 0 to 230 gm or 0 to 250 gms, with a least count of 5 gms.  We could also use a balance with a range of 0 to 500gms or 1000 gms with a least count of 5 gms. Such a balance is cheap and best.

   Then the balance will show 230 gms. Then the error will be only about 0.5 gms. The balance shown in the pic has a least count of 2gms.

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If we can afford a costlier balance, then we need to get a balance of range: 0 to 250 gms and least count = 0.5 gms.  This could be expensive. In this case there will be 500 readings on the scale. Perhaps we don't have  such a balance.  

Perhaps we find balances that have a scale on it having at most 100 readings. That means least count = range /100. 

*** In that case, we may have a spring balance of range 0 to 250 gm with a least count of 2.5 gms.  Or, a balance of range 0 to 500 gms with a least count of 5 gms.