Question 6

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 ?

Answer

A device with minimum count is the most suitable to measure length.

(a) Least count of vernier callipers

= 1 standard division (SD) -1 vernier division (VD)

= 1- 9/10 = 1/10 0.01 cm

(b) Least count of screw gauge = Pitch / Number of divisions

= 1/1000 = 0.001 cm

(c) Least count of an optical device = Wavelength of light ≈ 10^{-5} cm

= 0.00001 cm

Hence, it can be inferred that an optical instrument is the most suitable device to measure length.

- 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:-
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}. - 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:- 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:-
The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

- Q:- Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg,

(a) just after it is dropped from the window of a stationary train,

(b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,

(c) just after it is dropped from the window of a train accelerating with 1 m s 2,

(d) lying on the floor of a train which is accelerating with 1 m s 2, the stone being at rest relative to the train. Neglect air resistance throughout. - 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:-
A woman starts from her home at 9.00 am, walks with a speed of 5 km h

^{-1}on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 km h^{-1}. Choose suitable scales and plot the x-t graph of her motion. - Q:-
A steam engine delivers 5.4 x 10

^{8}J of work per minute and services 3.6 x 10^{9 }J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?

- Q:- Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg,

(a) just after it is dropped from the window of a stationary train,

(b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,

(c) just after it is dropped from the window of a train accelerating with 1 m s 2,

(d) lying on the floor of a train which is accelerating with 1 m s 2, the stone being at rest relative to the train. Neglect air resistance throughout. - Q:-
During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000 Pa. At what height must the blood container be placed so that blood may just enter the vein? [Use the density of whole blood from Table 10.1].

- Q:-
Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said : “The most incomprehensible thing about the world is that it is comprehensible”?

- Q:-
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}. - Q:-
When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of Jupiter.

- Q:-
Figure 3.25 gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at the points A, B, C and D?

- Q:-
A player throws a ball upwards with an initial speed of 29.4 m s

^{–1}. What is the direction of acceleration during the upward motion of the ball? What are the velocity and acceleration of the ball at the highest point of its motion?Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion. To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 m s

^{–2}and neglect air resistance). - 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:-
Fill in the blanks

(a) The volume of a cube of side 1 cm is equal to.....m

^{3}(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ... (mm)

^{2 }(c) A vehicle moving with a speed of 18 km h

^{–1}covers....m in 1 s(d) The relative density of lead is 11.3. Its density is ....g cm

^{–3}or . ...kg m^{–3}. - Q:-
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

- NCERT Chapter

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