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:- 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 transverse harmonic wave on a string is described by

y(x,t) = 3.0 sin [36t + 0.018x + π /4]

Where x and y are in cm and t in s. The positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?

(b) What are its amplitude and frequency?

(c) What is the initial phase at the origin?

(d) What is the least distance between two successive crests in the wave?

- Q:- Read each statement below carefully and state with reasons, if it is true or false:

(a) The magnitude of a vector is always a scalar

(b) each component of a vector is always a scalar

(c) the total path length is always equal to the magnitude of the displacement vector of a particle

(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time

(e) Three vectors not lying in a plane can never add up to give a null vector.

- Q:-
A vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors a and b at different locations in space necessarily have identical physical effects? Give examples in support of your answer.

- Q:-
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?

- Q:-
A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey

(a) climbs up with an acceleration of 6 m s

^{-2}(b) climbs down with an acceleration of 4 m s

^{-2}(c) climbs up with a uniform speed of 5 m s

^{-1}(d) falls down the rope nearly freely under gravity?

(Ignore the mass of the rope).

- Q:- State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

(a) adding any two scalars,

(b) adding a scalar to a vector of the same dimensions,

(c) multiplying any vector by any scalar,

(d) multiplying any two scalars,

(e) adding any two vectors,

(f) adding a component of a vector to the same vector. - Q:-
A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m

^{2}s^{–2}. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α^{–1}β^{– 2}γ^{2}in terms of the new units. - Q:-
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- Q:-
Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m. Give the magnitude and direction of

(a) the force on the 7

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^{th}coin by the eighth coin,(c) the reaction of the 6

^{th }coin on the 7^{th}coin. - Q:-
Write in about 1000 words a fiction piece based on your speculation on the science and technology of the twenty-second century.

- Q:-
Look at the graphs (a) to (d) (Fig. 3.20) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle.

**(a)** - Q:-
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.

pranav
2021-06-18 19:16:03

excellent explanation ever seen

- NCERT Chapter