﻿ A man walking briskly in rain with speed v must slant his umbrella forward making an angle  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.  from Physics Units and Measurement Class 11 CBSE
A man walking briskly in rain with speed v must slant his umbrella forward making an angle  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.

The relation tan  = v is wrong because the dimensions on both the sides of the equation are not equal.

Dimension of right hand side is [MoL1T-1

Dimension of Left hand side quantity is [MoLoTo

Hence, the equation is wrong.

To make the relation dimensionally correct, R.H.S should be divided by the speed of the rainfall.

That is,

, is a dimensionally correct relation.
521 Views

State the number of significant figures in the following : (a) 0.007 m (b) 2.64  kg (c) 0.2370 g cm-3 d) 6.320 J e)   6.032 N m-
f)  0.0006032 m2

The number of significant figures are:

(a) One (b) Three (c) Four d) Three e) Four f) seven
441 Views

A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2 sñ2. Suppose we employ a system of units in which the unit of mass equals αkg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2  in terms of the new units.

We know that dimensional formula of heat energy is

It is given that,

1 cal = 4.2J

In SI system,

M= 1 kg, L= 1 m,  T= 1 s

In new system of units,

We  know,

403 Views

Fill in the blanks :
c) A vehicle moving with a speed of 18 km h–1covers....m in 1 s

Tips: -

190 Views

The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to
...(mm)2

1.5 x 104 mm2

The total surface area of a cylinder of radius r and height h is

S = 2πr (r + h).

265 Views

Fill in the blanks:
a) The volume of a cube of side 1 cm is equal to .....m3

10-6

1 cm =

223 Views