Question 1

The figure shows the position-time (x-t) graph of one-dimenstional motion of a body of mass  0.4kg . The magnitude of each impulse is

Accepted Answer

ext { impulse }=\Delta p=m \Delta v u=\dfrac{2-0}{2-0}=1 v=\dfrac{2-4}{2-0}=-1 \Delta v=1-(-1) =2

Δ p = 0.4 \times 2 = 0.8 N S

Question 2

The sides of a rectangle are  7.01\ m  and  12\ m . Taking the significant figures into account, the area of the rectangle is

Accepted Answer

Given,side of rectangle are  7.01\ m  and  12\ m .Area of rectangle  = Length	imes Breadth = 7.01	imes 12 = 84.12\ m^{2} Rounded of two significant figures.Area of rectangle  = 84\ m^{2} .

Question 3

With due regard to significant figures, add the following:a. 953 and 0.324b. 953 and 0.625c. 953.0 and 0.324d. 953.0 and 0.374

Accepted Answer

a.   953+0.324=953.324\approx \boxed { 953 }  b.   953+0.625=953.625\approx \boxed { 954 }  c.   953.0+0.324=953.324\approx \boxed { 953.3 }  d.   953.0+0.374=953.374\approx \boxed { 953.4 }

Question 4

The numbers 3.845 and 3.835 on rounding off to 3 significant figures will give then

Accepted Answer

The number 3.845 rounded off to three significant figures becomes 3.84 since the preceding digit is even. On the other hand, the number 3.835 rounded off to three significant figures becomes 3.84 since the preceding digit is odd.

Question 5

A physical quantity P is related to four observables a, b, c and d as follows :
P $a^{3} b^{2}$ / $c$ d
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 ?

Accepted Answer

P = \dfrac{a^3 b^2}{\sqrt{c}  d}  Maximum fractional error in P is given by \dfrac{\Delta P}{P} = \pm \left[3\dfrac{\Delta a}{a} + 2\dfrac{\Delta b}{b}+ \dfrac{1}{2}\dfrac{\Delta c}{c}+ \dfrac{\Delta d}{d}\right] On putting above value:         = \pm \dfrac{13}{100} = 0.13  Percentage error in  P = 13  %Value of P is given as 3.763.By rounding off the given value to the first decimal place, we get  P = 3.8 .

Question 6

The mass of a box measured by a grocer's balance is  2.3\ kg . two gold pieces of masses  20.15\ g  and  20.17\ g  are added to the box. The total mass of the box is:

Accepted Answer

Mass of the box measured       m_1 = 2.3   kg Mass of the one gold piece       m_2 = 20.15   g     = 0.02015     kg Mass of the second gold piece       m_3 = 20.17   g     = 0.02017     kg Total mass of the box      M = m_1 + m_2 + m_3 	herefore    M = 2.3 + 0.02015 + 0.02017   =  2.34032   kg But as among all the masses, the mass  2.3 kg  contains one significant figure after decimal. So we need to round off the final answer upto one decimal place.  \implies      M = 2.3   kg

Important questions on Rounding Of Digits

The figure shows the position-time (x-t) graph of one-dimenstional motion of a body of mass $0.4 k g$ . The magnitude of each impulse is

$0.2 N s$

$0.4 N s$

$0.8 N s$

$1.6 N s$

The sides of a rectangle are $7.01 m$ and $12 m$ . Taking the significant figures into account, the area of the rectangle is

$84.1 m^{2}$

$84.00 m^{2}$

$84.12 m^{2}$

$84 m^{2}$

With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374

a. $953$ ; b. $954$ c. $953.3$ d. $953.4$

a. $953$ ; b. $955$ c. $953.3$ d. $953.4$

a. $952$ ; b. $954$ c. $953.3$ d. $953.4$

a. $953$ ; b. $954$ c. $953.3$ d. $952.4$

The numbers 3.845 and 3.835 on rounding off to 3 significant figures will give then

3.85 and 3.84

3.84 and 3.83

3.85 and 3.83

3.84 and 3.84

The mass of a box measured by a grocer's balance is $2.3 k g$ . two gold pieces of masses $20.15 g$ and $20.17 g$ are added to the box. The total mass of the box is:

$2.30 k g$

$2.340 k g$

$2.34 k g$

$2.3 k g$

More important questions

Important questions on Rounding Of Digits

The figure shows the position-time (x-t) graph of one-dimenstional motion of a body of mass 0.4kg. The magnitude of each impulse is

0.2Ns

0.4Ns

0.8Ns

1.6Ns

The sides of a rectangle are 7.01 m and 12 m. Taking the significant figures into account, the area of the rectangle is

84.1 m2

84.00 m2

84.12 m2

84 m2

With due regard to significant figures, add the following: a. 953 and 0.324 b. 953 and 0.625 c. 953.0 and 0.324 d. 953.0 and 0.374

a. 953; b. 954 c. 953.3 d. 953.4

a. 953; b. 955 c. 953.3 d. 953.4

a. 952; b. 954 c. 953.3 d. 953.4

a. 953; b. 954 c. 953.3 d. 952.4

The numbers 3.845 and 3.835 on rounding off to 3 significant figures will give then

3.85 and 3.84

3.84 and 3.83

3.85 and 3.83

3.84 and 3.84

The mass of a box measured by a grocer's balance is 2.3 kg. two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box is:

2.30 kg

2.340 kg

2.34 kg

2.3 kg

More important questions

The figure shows the position-time (x-t) graph of one-dimenstional motion of a body of mass $0.4 k g$ . The magnitude of each impulse is

$0.2 N s$

$0.4 N s$

$0.8 N s$

$1.6 N s$

The sides of a rectangle are $7.01 m$ and $12 m$ . Taking the significant figures into account, the area of the rectangle is

$84.1 m^{2}$

$84.00 m^{2}$

$84.12 m^{2}$

$84 m^{2}$

With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374

a. $953$ ; b. $954$ c. $953.3$ d. $953.4$

a. $953$ ; b. $955$ c. $953.3$ d. $953.4$

a. $952$ ; b. $954$ c. $953.3$ d. $953.4$

a. $953$ ; b. $954$ c. $953.3$ d. $952.4$

The mass of a box measured by a grocer's balance is $2.3 k g$ . two gold pieces of masses $20.15 g$ and $20.17 g$ are added to the box. The total mass of the box is:

$2.30 k g$

$2.340 k g$

$2.34 k g$

$2.3 k g$