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?
Round up the following upto three significant figures:
2808
How many significant figures should be present in the answer of the following calculation?
0.0125 + 0.7864 + 0.0215
The relative density of lead is 11.3. Its density is ______ g cm–3or ______ kg m–3.
Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.
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?
A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine? (Speed of sound in water = 1450 m s–1).
State the number of significant figures in the following:
0.007 m2
Solve the numerical example.
Write down the number of significant figures in the following: 0.003 m2, 0.1250 gm cm-2, 6.4 x 106 m, 1.6 x 10-19 C, 9.1 x 10-31 kg.
Answer the following question.
Describe what is meant by order of magnitude.
The radius of the circle is 3.12 m. Calculate the area of the circle with regard to significant figures.
Write the rules for determining significant figures.
Write a short note on the following.
Rounding - off
How many significant figures should be present in the answer of the following calculations?
`(2.5 xx 1.25 xx 3.5)/2.01`
Taking into account of the significant figures, what is the value of 9.99 m – 0.0099 m?
The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is ______.
The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give ______.
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.
Using the rules for significant figures, the correct answer for the expression `(0.02858 xx 0.112)/(0.5702)` will be ______.
Significant figures in a measurement include which of the following?
The arithmetic mean of three measurements, 15.4 cm, 15.4 cm, and 15.5 cm, is 15.43 cm. How many significant figures does this result have?
How many significant figures are there in the number 0.001405?
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?
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?
