Significant Figures in Product

Q. In a particular system, the unit of length, mass and time are chosen to be $10\text{cm}$, $10\text{gm}$ and $0.1\text{s}$ respectively. The unit of force in this system will be equivalent to

1. $1\text{N}$
2. $10\text{N}$
3. $100\text{N}$
4. $1/10\text{N}$

Q.

Using a screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as

1. 2.125 cm

2. 2.124 cm

3. 2.123

4. 2.121 cm

Q. If $97.52$ is divided by $2.54$, the correct result in terms of significant figures is

1. $38.4$
2. $38.3937$
3. $38.394$
4. $38.39$

Q. Find the maximum percentage error in the measurement of pressure, if maximum errors in the measurement of force and length of a square plate are $3$% and $2$% respectively.

1. $3$%
2. $5$%
3. $7$%
4. $6$%

Q. The mass and volume of a body are $4.237\text{g}$ and $2.5{\text{cm}}^3$ respectively. The density of the material of the body in correct significant figures is

1. $1.6948{\text{g/cm}}^3$
2. $1.69{\text{g/cm}}^3$
3. $1.7{\text{g/cm}}^3$
4. $1.695{\text{g/cm}}^3$

Q. A thin cylindrical wire has a length of $21.7\text{cm}$ and radius of $0.46\text{mm}$. The volume of the thin wire to the correct significant figures is

1. $0.1{\text{cm}}^3$
2. $0.14{\text{cm}}^3$
3. $0.144{\text{cm}}^3$
4. $0.1443{\text{cm}}^3$

Q.

A student has measured the length of a wire equal to $0.04580m$. This value of length has the number of significant figures equal to

1. five

2. four

3. six

4. None of these

Q. If a body travels a distance of $97.52\text{m}$ along a straight line in $2.54\text{s}$, then its speed in appropriate significant figures is

1. $38.4\text{m/s}$
2. $38.3937\text{m/s}$
3. $38.39\text{m/s}$
4. $38.394\text{m/s}$

Q.

Name three derived physical quantities

Q. The length of a strip measured with a meter rod is 10.0 $cm$. Its width mesasured with a vernier callipers is 1.00 $cm$. The least count of metre rod is 0.1 $cm$ and that of vernier calliipers is 0.01 $cm$. What will be the error in its area?

1. $\pm 0.01c{m}^2$
2. $\pm 0.1c{m}^2$
3. $\pm 0.11c{m}^2$
4. $\pm 0.2c{m}^2$

Q. There is screw gauge having main scale division as well as pitch of circular scale is 0.5 mm. Circular scale has 100 divisions. If no object is placed then ‘0’ of main scale is not visible and 3 division lies below reference main scale if wire is placed in between jaws, reading on main scale is 5.5 mm and ${48}^{th}$ division matches with reference on main scale. The diameter of wire is

1. 7.235 mm
2. 6.225 mm
3. 5.634 mm
4. 6.125 mm

Q. If a bucket of paint of 4.28 litres covers wall area of 48.0 $m^2,$ what is the thickness of layer of paint on the wall?

1. $8.9\times {10}^{-2}$ mm
2. $8.90\times {10}^{-2}$ mm
3. $9\times {10}^{-2}$ mm
4. None

Q. The sides of rectangle are given by 23.7 units and 3.8 units. Find the area of rectangle and specify correct number of significant figures .

1. 90.06 sq.units
2. 90.1 sq.units
3. $9.0\times {10}^1$ sq.units
4. none

Q. The length and the breadth of a rectangular sheet are $16.2\text{cm}$ and $10.1\text{cm}$ respectively. The area of the sheet in appropriate significant figures is

1. $164{\text{cm}}^2$
2. $163{\text{cm}}^2$
3. $163.6{\text{cm}}^2$
4. $163.62{\text{cm}}^2$

Q. The variation of density of a cylindrical thick and long rod, is $\rho ={\rho }_0\frac{x^2}{L^2}$, then position of its centre of mass from $x=0$ ens is :-

1. $2L/3$
2. $L/2$
3. $L/3$
4. $3L/4$

Q.

Define the least count of a screw gauge.

Q. An insect of negligible mass is sitting on a block of mass m, tied to an ideal spring as shown in the figure. The force constant of spring is k. The block performs simple harmonic motion with amplitude A in front of a plane mirror placed as shown in the figure. The maximum speed of insect relative to its image will be

1. $A\sqrt{\frac{k}{m}}$
2. $A\sqrt{2}\sqrt{\frac{k}{m}}$
3. $A\sqrt{\frac{m}{k}}$
4. $\frac{A}{\sqrt{2}}\sqrt{\frac{k}{m}}$

Q. A particle executing SHM has velocities $20$ cm/s and $16$ cm/s at displacements $4$ cm and $5$ cm from its mean position respectively. Its time period is

1. $\pi$ s
2. $2\pi$ s
3. $\pi /2$ s
4. $\pi /4$ s

Q. Figure below shows the reading obtained while measuring the diameter of a wire with a screw gauge. The screw advances by 1 division on main scale when circular head is rotated once.
Find: (i) pitch of the screw gauge,
(ii) Least count of the screw gauge, and
(iii) The diameter of the wire.

Q. A screw gauge has pitch of $1.0mm$ & $80$ divisions on its circular scale. When a coin is fitted between its studs, it reads $8$ main scale divisions & $48$ divisions on circular scale, with no zero error. The reading of screw gauge is

1. $8.6mm$
2. $8.48mm$
3. $8.80mm$
4. $8.32mm$

Q. A body executing SHM has its velocity $10cm/s$ and $7cm/s$ when its displacements from mean position are $3cm$ and $4cm$ respectively. The length of path is

1. $10cm$
2. $9.5cm$
3. $4cm$
4. $11.36cm$

Q. A stop watch has a circular dial divided into 120 divisions. What is its least count?

Q.

What is meant by the pitch of a screw?

Q. A base plate of $460\times 400mm$ is to be provided below a column section ISHB 300@ 576.83 N/m. The bearing pressure from concrete below the base plate is $8.8N/m{m}^2$. The suitable thickness of the base plate will be
[Take, $b_f=250\text{mm},t_f=10.6\text{mm},t_w=7.6\text{mm},{\gamma }_{m0}=1.1,f_y=250\text{MPa}]$

1. $20\text{mm}$
2. $22\text{mm}$
3. $24\text{mm}$
4. $26\text{mm}$

Q. The area of a rectangular field (in ${\text{m}}^2$ ) of length $55.3\text{m}$ and breadth $25\text{m}$ after rounding off the value for correct significant digits is

1. $1382.5$
2. $14\times {10}^2$
3. $1382$
4. $138\times {10}^1$

Q. In above problem choose the correct value(s) of $F$ which the blocks $M$ and $m$ remain stationary with respect to $M_0$

1. $(M_0+M+m)\frac{g}{\mu }$
2. $\frac{m(M_0+M+m)g}{M-\mu m}$
3. $(M_0+M+m)\frac{mg}{M}$
4. None of these

Q. If the least count of a stop clock is $0.5s$, then what are the number of divisions on the watch?

1. $60$
2. $120$
3. $240$
4. $360$

Q. A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is:

1. $\frac{1}{2}$
2. $\frac{1}{3}$
3. $\frac{1}{6}$
4. $\frac{1}{4}$

Q. A mass of 2 kg falls from a height of 40 cm, on a spring with a force constant of 1960 N/m. The spring is compressed by ? (Take $g=9.8m/s^2$)

1. 10 cm
2. 1.0 cm
3. 20 cm
4. 5 cm

Q. The sides of rectangle are given by 23.7 units and 3.8 units. Find the area of rectangle and specify correct number of significant figures .

1. 90.06 sq.units
2. 90.1 sq.units
3. $9.0\times {10}^1$ sq.units
4. none