Question 2

Fill in the blanks by suitable conversion of units:

(a) 1 kg m^{2}s^{–2}= ....g cm^{2 }s^{–2 }

(b) 1 m =..... ly

(c) 3.0 m s^{–2}=.... km h^{–2}

(d) G = 6.67 × 10^{–11} N m^{2} (kg)^{–2}=.... (cm)3s^{–2} g^{–1}.

Answer

(a) 1 kg = 10^{3} g

1 m^{2} = 10^{4} cm^{2 }

1 kg m^{2} s^{–2} = 1 kg × 1 m^{2} × 1 s^{–2}

=10^{3 }g × 10^{4} cm^{2} × 1 s^{–2} = 10^{7} g cm^{2} s^{–2}

1 kg m^{2}s^{–2} = 10^{7} g cm^{2} s^{–2}

(b) Distance = Speed × Time

Speed of light = 3 × 10^{8} m/s

Time = 1 year = 365 days = 365 × 24 hours = 365 × 24 × 60 × 60 sec

Putting these values in above formula we get

1 light year distance = (3 × 10^{8} m/s) × (365 × 24 × 60 × 60 s) = 9.46 × 1015 m 9.46 × 10^{15} m = 1 ly

So that 1 m = 1/ 9.46 × 10^{15} ly = 1.06 × 10^{-16} ly

(c) 1 hour = 3600 sec so that 1 sec = 1/3600 hour

1 km = 1000 m so that 1 m = 1/1000 km

3.0 m s^{–2} = 3.0 (1/1000 km)( 1/3600 hour)^{-2} = 3.0 × 10^{–3} km × ((1/3600)^{-2} h^{–2})

= 3.0 × 10^{–3} km × (3600)^{2} h^{–2} = 3.88 × 10^{4} km h^{–2} 3.0 m s^{–2}

= 3.88 × 10^{4} km h^{–2}

(d) Given,

G= 6.67 × 10^{–11} N m^{2} (kg)^{–2}

We know that

1 N = 1 kg m s^{–2}

1 kg = 10^{3} g

1 m = 100 cm = 10^{2} cm

Putting above values,we get

6.67 × 10^{–11} N m^{2} kg^{–2} = 6.67 × 10^{–11} × (1 kg m s^{–2}) (1 m^{2}) (1Kg^{–2})

Solve and cancel out the units we get

⇒ 6.67 × 10^{–11} × (1 kg^{–1} × 1 m^{3} × 1 s^{–2})

Putting above values to convert Kg to g and m to cm

⇒ 6.67 × 10^{–11} × (10^{3} g)^{-1} × (10^{2} cm)^{3} × (1 s^{–2})

⇒ 6.67 × 10^{–11 }× 10^{-3} g^{-1} × 10^{6} cm^{3} × (1 s^{–2})

⇒ 6.67 × 10^{–8} cm3 s^{–2} g^{–1}

G = 6.67 × 10^{–11} N m^{2} (kg)^{–2}

= 6.67 × 10^{–8} (cm)3s^{–2} g–1.

- Q:-
State the number of significant figures in the following:

(a) 0.007 m

^{2}(b) 2.64 x 10

^{24}kg(c) 0.2370 g cm

^{-3}(d) 6.320 J

(e) 6.032 N m

^{-2}(f) 0.0006032 m

^{2} - Q:-
A physical quantity P is related to four observables a, b, c and d as follows :

The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?

- Q:-
Rain is falling vertically with a speed of 30 m s

^{–1}. A woman rides a bicycle with a speed of 10 m s^{–1}in the north to south direction. What is the direction in which she should hold her umbrella? - Q:-
Toricelli's barometer used mercury. Pascal duplicated it using French wine of density 984 kg m

^{-3}. Determine the height of the wine column for normal atmospheric pressure. - Q:- Give the magnitude and direction of the net force acting on

(a) a drop of rain falling down with a constant speed

(b) a cork of mass 10 g floating on water

(c) a kite skillfully held stationary in the sky

(d) a car moving with a constant velocity of 30 km/h on a rough road

(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields. - Q:-
The mass of a box measured by a grocer's balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is

(a) the total mass of the box,

(b) the difference in the masses of the pieces to correct significant figures?

- Q:-
On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

- Q:-
What amount of heat must be supplied to 2.0 x 10

^{-2}kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N^{2}= 28; R = 8.3 J mol^{-1}K^{-1}.) - Q:- In which of the following examples of motion, can the body be considered approximately a point object:

(a) a railway carriage moving without jerks between two stations.

(b) a monkey sitting on top of a man cycling smoothly on a circular track.

(c) a spinning cricket ball that turns sharply on hitting the ground.

(d) a tumbling beaker that has slipped off the edge of a table. - Q:-
A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is

(a) at the end A,

(b) at the end B,

(c) at the mid-point of AB going towards A,

(d) at 2 cm away from B going towards A,

(e) at 3 cm away from A going towards B, and

(f) at 4 cm away from B going towards A.

- Q:-
Explain why: (a) a body with large reflectivity is a poor emitter (b) a brass tumbler feels much colder than a wooden tray on a chilly day (c) an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open, but gives a correct value for the temperature when the same piece is in the furnace (d) the earth without its atmosphere would be inhospitably cold (e) heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water

- Q:-
The mass of a box measured by a grocer's balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is

(a) the total mass of the box,

(b) the difference in the masses of the pieces to correct significant figures?

- Q:-
Which of the following is the most precise device for measuring length:

(a) a vernier callipers with 20 divisions on the sliding scale

(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale

(c) an optical instrument that can measure length to within a wavelength of light ?

- Q:-
Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m

^{3}at a temperature of 27 °C and 1 atm pressure. - Q:-
Establish the following vector inequalities geometrically or otherwise:

(a) |a + b| ≤ |a| + |b|

(b) |a + b| ≥ ||a| − |b||

(c) |a − b| ≤ |a| + |b|

(d) |a − b| ≥ ||a| − |b||

When does the equality sign above apply?

- Q:-
**A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Fig. 5.19. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without the floor yielding?** - Q:- Explain why (or how):

(a) In a sound wave, a displacement node is a pressure antinode and vice versa,

(b) Bats can ascertain distances, directions, nature, and sizes of the obstacles without any eyes,

(c) A violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,

(d) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and

(e) The shape of a pulse gets distorted during propagation in a dispersive medium. - Q:-
Though the statement quoted above may be disputed, most physicists do have a feeling that the great laws of physics are at once simple and beautiful. Some of the notable physicists, besides Dirac, who have articulated this feeling, are : Einstein, Bohr, Heisenberg, Chandrasekhar and Feynman. You are urged to make special efforts to get access to the general books and writings by these and other great masters of physics.

(See the Bibliography at the end of this book.) Their writings are truly inspiring !

- Q:-
Figure 3.21 shows the x-t plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t > 0? If not, suggest a suitable physical context for this graph.

- Q:-
A jet airplane travelling at the speed of 500 km h

^{-1}ejects its products of combustion at the speed of 1500 km h^{-1}relative to the jet plane. What is the speed of the latter with respect to an observer on ground?

pranav
2021-06-18 19:16:03

excellent explanation ever seen

- NCERT Chapter