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Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

A rectangular vessel $ 1 m \times 0.6 m \times 0.5 m $ filled with maize grains. Treat the grains spheres of diameter 0.3 cm each.The number of grains in the vessel is the nearest to 

  1. $ 5 \times 10^7 $
  2. $ 1 \times 10^7 $
  3. $ 2 \times 10^7 $
  4. $ 2 \times 10^5 $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let n number of grains are in the vessel.

So, volume of cuboid vessel is equal to n times volume of spheres. i.e.

$ 1\times 0.6\times 0.5=n\left( \dfrac{4}{3}\times 3.14\times {{\left( \dfrac{3}{2000} \right)}^{3}} \right) $

$ 0.3=n\dfrac{4}{3}\times 3.14\times 3.375\times {{10}^{-9}} $

$ 0.3=n\times 14.13\times {{10}^{-9}} $

$ n=\dfrac{0.3}{14.13\times {{10}^{-9}}} $

$ n=0.021\times {{10}^{9}}\, $

$ n=2\times {{10}^{7}}$

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density
A single sheet of aluminium foil is folded twice to produce a stack of four sheets. The total thickness of the stack of sheets is measured to be $(0.80\pm 0.02)mm$. This measurement is made using a digital caliper with a zero error or $(-0.20\pm 0.02)mm$
What is the percentage uncertaintyin calculated thickness of a single sheet?
  1. $1.0$%
  2. $2.0$%
  3. $4.0$%
  4. $6.7$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The zero error (−0.20) can be removed but its uncertainty (± 0.02) must be added to the measurement uncertainty.

True value of total thickness =$ 0.80 + 0.20 = 1.0 mm  $

Total uncertainty in measurement = $(0.02+0.02)=0.04\ mm$

So the four sheets have a true thickness of $ (1.00 ± 0.04) mm.$
 A single sheet would have a thickness of $(0.25 ± 0.01) mm.$

Percentage error= $\dfrac{0.01}{0.25}\times 100 = 4.0$%

Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

The volume of water in a measuring cylinder is 55 mL When a stone tied to a string is immersed in the water the water level rises to 83 mL. Find the volume of the stone

  1. $28ml^2$
  2. $28ml$
  3. $38ml$
  4. $28m^2l$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Initial level of water  $v _i = 55 \ ml$
Final level of water  $v _f = 83  ml$
Volume of stone  $V _{stone} = V _f - V _i = 83 - 55 = 28 \ ml$
Multiple choice physics learning how to measure measurement of area and volume measurement of volume measurement of area, volume and density

A cubic metre of water at $0^o$C is solidified into ice, density of ice is $0.96$ of water at $0^o$C. Which of the following deductions are true?
$1$. Water expands when solidified.
$2$. Ice will float in water at $0^o$C with half its volume above the surface.
$3$. Density of all liquids are higher than its density when solidified.

  1. $3$ only
  2. $2$ only
  3. $1$ only
  4. $1$ and $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When water freezes into ice, its density decreases, meaning its volume increases (it expands). This expansion is a unique property of water. Statement 1 is true. Statement 2 is false because ice floats with about 90% of its volume submerged, not 50%. Statement 3 is false as a general rule.