Integration, Differentiation, Errors & Significant Figures MCQ Level - 1 (Test - 1) - Class 11 MCQ

A student uses a sim ple pendulum of exactly 1 m length to determine g, the acceleration due to gravity.He uses a stop watch with the least count of 1 s for this and records 40 s for 20 oscillations. For this observation, which of the following statements(s) is/are true?

A vernier callipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier callipers, the least count is

The respective num ber of significant figures for the numbers 23.02310.0003 and 2.1 x 10^-3 are ‘

A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 m. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm.The 5 sets of (u, v) values recorded by the student (in cm) are : (42, 56), (48, 48),(60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (=05°), then the least count of the instrument is

The percentage errors in the measurement of length and’ time period of a simple pendulum are 1% and 2% respectively. Then the maximum error in the measurement of acceleration due to gravity is

If 3.8 x 10^-6 is added to 4.2 x 10^-5 giving due regard to significant figures, then the result will be

The number of significant figures in the numbers 4.8000 x10⁴ and 48000.50 are respectively

A student has m easured the length of a wire equal to 0.04580 m. This value of length has the number of significant figure is equal to :

Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations.
The observations are shown in the table.
Least count for length = 0.1 cm.
Least count for time = 0.1 s.

If E_I, E_II and E_III are the percentage errors in g, ie, , for students I, II and III respectively..

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms^-1. The magnitude of its momentum is recorded as

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of -0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

If voltage V = (100 ± 5) volt and current I = (10 ± 0.2) A, the percentage error in resistance R is

A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ± 0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm ‘with an uncertainty of ± 0.01 mm. Take g = 9.8ms^-2 (exact). The Young’s modulus obtained from the reading is

The values of two resistors are R₁ = (6 ± 0.3)k Ω and R₂ = (10 ± 0.2)k Ω. The percentage error in the equivalent resistance when they are connected in parallel is

A physical quantity A 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%, 2% and 2% respectively. What is the percentage error in the quantity A ? 

A student performs an experiment for determination of , and he commits an error of Di . For T he takes the time of n oscillations with the stop watch of least count Δ T and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate?

The circular scale of a screw gauge has 50 divisions and pitch of 0.5 mm. Find the diameter of sphere. Main scale reading is 2.

If error in radius is 3%, what is error in volume of sphere?

The length of a simple pendulum is about 100 cm known to an accuracy of 1 mm. Its period of oscillation is 2s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g ?

A physical quantity is given by X =[M^aL^bT^c]. The percentage error in measurement of M, L and T are α,β and γ respectively. Then, the maximum % error in the quantity X is

If the length of a rectangle t = 10.5 cm, breadth b = 2.1 cm and minimum possible measurement by scale = 0.1 cm, then the area is