Advertisements
Advertisements
प्रश्न
A large ball 2 m in radius is made up of a rope of square cross-section with edge length 4 mm. Neglecting the air gaps in the ball, what is the total length of the rope to the nearest order of magnitude?
Advertisements
उत्तर
Given: r = 2 m
Area = A = 4 × 4 = 16 mm2 = 16 × 10−6 m2
Volume of ball = Volume enclosed by rope.
`4/3 pi` (radius)3 = Area of cross-section of rope × length of rope.
∴ length of rope l = `(4/3 pir^3)/A`
∴ l = `(4 xx 3.142 xx 2^3)/(3 xx 16 xx 10^-6)`
= `(cancel4 xx 3.142 xx 2 xx 2 xx 2)/(3 xx cancel16 xx 10^(-6))`
= `(3.142 xx cancel8)/(3 xx cancel4 xx 10^(-6))`
= `(3.142 xx 2)/(3) xx 10^6`m
≈ 2 × 106 m.
∴ Total length of rope to the nearest order of magnitude = 106 m = 103 km.
APPEARS IN
संबंधित प्रश्न
What do you mean by significant figures?
How many significant figures are present in the 208?
How many significant figures are present in the 500.0?
Round up the following upto three significant figures:
34.216
Round up the following upto three significant figures:
10.4107
The relative density of lead is 11.3. Its density is ______ g cm–3or ______ kg m–3.
The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?
The photograph of a house occupies an area of 1.75 cm2on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 m2. What is the linear magnification of the projector-screen arrangement?
A man walking briskly in rain with speed v must slant his umbrella forward making an angle θ with the vertical. A student derives the following relation between θ and v: tan θ = v and checks that the relation has a correct limit: as v →0, θ → 0, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct? If not, guess the correct relation.
Describe what is meant by significant figures.
Solve the numerical example.
Nuclear radius R has a dependence on the mass number (A) as R =1.3 × 10-16 A1/3 m. For a nucleus of mass number A = 125, obtain the order of magnitude of R expressed in the meter.
The radius of the circle is 3.12 m. Calculate the area of the circle with regard to significant figures.
If the density of a solution is 3.12 g mL–1, the mass of 1.5 mL solution in significant figures is ______.
The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give ______.
The length and breadth of a rectangular sheet are 16.2 cm and 10.1cm, respectively. The area of the sheet in appropriate significant figures and error is ______.
Why do we have different units for the same physical quantity?
Using the rules for significant figures, the correct answer for the expression `(0.02858 xx 0.112)/(0.5702)` will be ______.
Which of the following measurements has exactly two significant figures?
The radius of Earth is written as 0.64 × 10⁷ m in scientific notation. What is its order of magnitude?
How many significant figures are there in the number 0.001405?
Which of the following numbers has 4 significant figures?
The radius of Earth is expressed as 0.64 × 10⁷ m in scientific notation. What is its order of magnitude and number of significant figures?
Which of the following statements is correct about significant figures and accuracy?
