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
How many significant figures are present in the 0.0025?
How many significant figures are present in the 5005?
Round up the following upto three significant figures:
34.216
Round up the following upto three significant figures:
10.4107
Round up the following upto three significant figures:
2808
How many significant figures should be present in the answer of the following calculation?
5 × 5.364
The relative density of lead is 11.3. Its density is ______ g cm–3or ______ kg m–3.
You are given a thread and a metre scale. How will you estimate the diameter of the thread?
A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?
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.
A LASER is a source of very intense, monochromatic, and unidirectional beam of light. These properties of a laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. A laser light beamed at the Moon takes 2.56 s to return after reflection at the Moon’s surface. How much is the radius of the lunar orbit around the Earth?
It is a well known fact that during a total solar eclipse the disk of the moon almost completely covers the disk of the Sun. From this fact and from the information you can gather from examples 2.3 and 2.4, determine the approximate diameter of the moon.
State the number of significant figures in the following:
0.007 m2
State the number of significant figures in the following:
2.64 × 1024 kg
State the number of significant figures in the following:
6.032 N m–2
Describe what is meant by significant figures.
Answer the following question.
Describe what is meant by order of magnitude.
The mass and volume of a body are 4.237 g and 2.5 cm3, respectively. The density of the material of the body in correct significant figures is ______.
Why do we have different units for the same physical quantity?
Calculate the length of the arc of a circle of radius 31.0 cm which subtends an angle of `pi/6` at the centre.
Significant figures in a measurement include which of the following?
What is the least count of a measuring instrument?
How many significant figures are there in the number 0.001405?
Which of the following numbers has 4 significant figures?
Which of the following statements is correct about significant figures and accuracy?
A length L is measured as 125 m, which is also written as 12500 cm and 125000 mm. How many significant figures does this measurement have?
