In an experiment on determining density of a rectangular block, the dimensions of the block are mesured with vernier callipers `(V.C = 0.01 cm)` and its mass is measured with a beam balance `(L.C. = 0.1 g)`. The measured values are : Mass`(m) = 39.3` g Length`(l) = 5.12` cm Breadth`(b) = 2.56` cm Thickness`(t)=0.37` cm Calculate density of the block with permissible limits of error.

In an experiment on determining density of a rectangular block, the di

1.	In an experiment on determining density of a rectangular block, the dimensions of the block are mesured with vernier callipers `(V.C = 0.01 cm)` and its mass is measured with a beam balance `(L.C. = 0.1 g)`. The measured values are : Mass`(m) = 39.3` g Length`(l) = 5.12` cm Breadth`(b) = 2.56` cm Thickness`(t)=0.37` cm Calculate density of the block with permissible limits of error.
Answer» Density `(rho)= ("Mass")/("Volume")=m/(lxxbxxt)` `=39.3/(5.12xx2.56xx0.37)g cm^(-3)` `=8.1037 g cm^(-3)` `=8.1 g cm^(-3)` (rounding off the result) The maximum relative error in the density is given by `(Delta rho)/rho=(Delta m)/m+(Delta l)/(l)+(Delta b)/b+(Delta t)/t` `=0.1/39.3+0.01/5.12+0.01/2.56+0.01/0.37` `=0.0024+0.0019+0.0039+0.027` `=0.0358` `:. " "Delta rho =0.0358 rho=0.0358xx8.1037 cong 0.3 g cm^(-3)` Thus, the density of the solid is `(8.1 pm 0.3)g cm^(-3)` Note : The main contribution to the relative error comes from the measurement of thickness (t). Hence, precision in the measurement of density can be increased by measuring thickness with screw gauge (L.C. = 0.001 cm) instead of vernier callipers (V.C. = 0.01 cm). experimentalists keep such facts in mind while carrying out different measurements in a given experiment.

Discussion

No Comment Found

Related InterviewSolutions

A vernier calipers has `1mm `marks on the main scale. It has `20` equal divisions on the Verier scale which match with `16` main scale divisions. For this Vernier calipers, the least count isA. 0.02 mmB. 0.05 mmC. 0.1 mmD. 0.2 mm
A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading =58.5 degree Vernier scale reading =0.9 divisions Given that 1 divisions on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. the angle of the prism from the above data is :A. `58.59^(@)`B. `58.77^(@)`C. `58.65^(@)`D. `59^(@)`
In `u-v` method for finding the focal length of a concave mirror. The mirror is fixed at position `A` marked `20.0cm` on an optical bench and an object needle is placed at position `B` marked `45.0cm` on an optical banch. For no parallax between object needle and image needle the image needle at position `C 57.5cm` on optical bench. Then percentage error in the measurement of focal length of the mirror is
A student performs an experiment for determination of ` g [ = ( 4 pi^(2) L)/(T^(2)) ] , L ~~ 1m` , and he commits an error of `Delta L`. For `T` he takes the time of `n` oscillations with the stop watch of least count ` Delta T` . For which of the following data , the measurement of `g` will be most accurate ?A. `DeltaL=0.5, DeltaT=0.1, n=20`B. `DeltaL=0.5, DeltaT=0.1, n=50`C. `DeltaL=0.5, DeltaT=0.01, n=20`D. `DeltaL=0.5, DeltaT=0.05, n=50`
In determination of value of acceleration due to gravity (g) by simple pendulum, the time period is measured by a topwatch (L.C. = 0.5 second) and length of the thread is measured with metre scale (L.C. 0.1 cm) and diametre of bob is measured with vernier callipers (L.C. = 0.1 cm). The following observations are recorded : Length of the thread `=105.3 cm` Diameter of the bob `=2.45 cm` Time period `=2.07 s` Number of oscillations `=10` Calculate the value of g, estimate error and write the result in proper significant figures.
A student uses a simple pendulum of exactly `1m` length to determine `g`, the acceleration due ti gravity. He uses a stop watch with the least count of `1sec` for this and record `40 seconds` for `20` oscillations for this observation, which of the following statement `(s) is (are)` true?A. Error `DeltaT` in measuring T, the time period, is 0.05 sB. Error `DeltaT` in measuring T, the time period is, 1 sC. Percentage error in the determination of g is 5%D. Percentage error in the determination of g is 2.5 %
Student `I ,II , and III` perform an experiment for measuring the acceleration due to gravity `(g) ` usinf a simple pendulum. They use lengths of the pendulum and // or record time for different number of oscillations . The observations are shown in the following table . Least count for length ` = 0.1 cm` `{:(underset(III)underset(II)underset(I)underset()underset()("Student"),underset(20.0)underset(64.0)underset(64.0)underset((cm))underset("Pendulam")("Length of "),underset(4)underset(4)underset(8)underset((n))underset("n Oscillation")("Number of"),underset(9.0)underset(16.0)underset(16.0)underset((s))underset("Period")("Time")):}` Least count for time `= 0.1 s`. If `E_(I), E_(II)` , and `E_(III)` are the percentage errors in `g` , i.,e., `((Delta g)/( g) xx 100)` for students I,II , and III, respectively , thenA. `E_(I)=0`B. `E_(I)` is minimumC. `E_(I)=E_(II)`D. `E_(II)` is maximum
A quantity X is given by `in_(0) L(DeltaV)/(Delta t)`, where `in_(0)` is the permittivity of free space, L is a length, `DeltaV` is a potential difference and `Delta t` is a time interval. The dimensional formula for X is the same as that of -
The dimensions of `1/2 in_(0) E^(2)` (`in_(0)`: permittivity of free space, E: electric field) is-A. `[MLT^(-1)]`B. `[ML^(2)T^(-2)]`C. `[ML^(-1)T^(-2)]`D. `[ML^(2)T^(-1)]`
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. A. 1.2 mmB. 1.25 mmC. 2.20 mmD. 2.25 mm

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment