A wire has a mass (0.3 ± 0.003)g, radius (0.5 ± 0.005)mm and length (6 ± 0.06)cm. The maximum percentage error in the measurement of its density is :
A vernier calipers has 1 mm marks on the main scale. It has 20 equal division on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is :
Unit of diploe moment is :
The length, breadth and thickness of a block are given by l = 12cm, b = 6 cm and t = 2.45 cm. The volume of the block according to the idea of significant figures should be :
An ice-cube of density 900 kg/m³ is floating in water of density 1000 kg/m³. The percentage of volume of ice-cube outside the water is :
If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is
The energy of a system as a function of time t is given as E(t) = A²exp(–at), where a = 0.2s–¹. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t = 5 s is
A body of uniform cross-sectional area floats in a liquid of density thrice its value. The fraction of exposed height will be :
Meter bridge is used to find resistance of a wire using a standard resistance 20Ω with 0.5% tolerance. The unknown resistance is placed in left gap of the meter bridge. The null point is obtained at 60.0 cm from left end. The maximum permissible error in this measurement is 0.1 cm. Find the maximum error in measurement of the resistance
Two full turns of the circular scale of a screw gauge cover a distance of 1mm 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 :
An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance is measured by
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 ( 0.5°), then the least count of the instrument is:
In an optics experiment, with the position of the object fixed, a student varies the position of the convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 45° with the x-axis meets the experimental curve at P. The coordinates of P will be:
A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10–³are
A screw gauge gives the following reading when used to measure the diameter of a wire . Main scale reading : 0 mm Circular scale reading : 52 division Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is :
If 400Ω of resistance is made by adding four 100 Ω resistances of tolerance 5%, then the tolerance of the combination is :
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is :
The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet are 5.5 mm and 48 respectively, the thickness of this sheet is :
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 μm diameter of a wire is:
In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :
In the density measurement of a cube, the mass and edge length are measured as (10.00 ±10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is :
The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is :
A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is :
