Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर १
Incorrect; on dimensional ground
The relation is `tan theta = v`.
Dimension of R.H.S = M0 L1 T–1
Dimension of L.H.S = M0 L0 T0
(∵ The trigonometric function is considered to be a dimensionless quantity)
Dimension of R.H.S is not equal to the dimension of L.H.S. Hence, the given relation is not correct dimensionally.
To make the given relation correct, the R.H.S should also be dimensionless. One way to achieve this is by dividing the R.H.S by the speed of rainfall V'.
Therefore, the relation reduces to
`tan theta = v/v'` This relation is dimensionally correct.
उत्तर २
According to principle of homogenity of dimensional equations,
Dimensions of L.H.S. = Dimensions of R.H.S.
Here, v = tan θ
i. e., [L1 T-1] = dimensionless, which is incorrect.
Correcting the L.H.S., we. get
v/u= tan θ, where u is velocity of rain.
संबंधित प्रश्न
How many significant figures are present in the 0.0025?
How many significant figures are present in the 208?
How many significant figures are present in the 500.0?
How many significant figures should be present in the answer of the following calculation:-
`(0.02856 xx 298.15 xx 0.112)/0.5785`
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?
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?
The length, breadth, and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.
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:
2.64 × 1024 kg
State the number of significant figures in the following:
6.320 J
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?
Write the rules for determining significant figures.
The number of significant figures in 0.06900 is ______.
The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is ______.
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 ______.
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 ______.
How many significant figures are there in the number 0.001405?
Which of the following statements is correct about significant figures and accuracy?
