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
What do you mean by significant figures?
How many significant figures are present in the 208?
How many significant figures are present in the 2.0034?
Round up the following upto three significant figures:
2808
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?
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?
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 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:
0.2370 g cm–3
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.
Solve the numerical example.
The diameter of a sphere is 2.14 cm. Calculate the volume of the sphere to the correct number of significant figures.
The radius of the circle is 3.12 m. Calculate the area of the circle with regard to significant figures.
How many significant figures should be present in the answer of the following calculations?
`(2.5 xx 1.25 xx 3.5)/2.01`
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 ______.
Why do we have different units for the same physical quantity?
Significant figures in a measurement include which of the following?
Which of the following numbers has 4 significant figures?
