What are the dimensions of the quantity l l g l being the length and g the acceleration due to gravity?

We know that the dimensions of acceleration due to gravity is given by, g = M 0 L 1 T - 2 The dimension of a given quantity is = L 1 L 1 M 0 L 1 T - 2 = M 0 L 1 T 1 Hence, the dimensions of a given physical quantity M 0 L 1 T 1 .

What are the dimensions of the quantity l l g l being the length and g the acceleration due to gravity?

We know that the dimensions of acceleration due to gravity is given by, g = M 0 L 1 T - 2 The dimension of a given quantity is = L 1 L 1 M 0 L 1 T - 2 = M 0 L 1 T 1 Hence, the dimensions of a given physical quantity M 0 L 1 T 1 .

If the measured values of two quantities are A ± ∆ A a n d B ± ∆ B being the mean absolute errors. What is the maximum possible error in A ± B Show that if Z = A B ∆ Z Z = ∆ A A + ∆ B B

If the measured value two physical quantities are A ± △ A and B ± △ B being the mean absolute error. Z = A B Z ± △ Z = A ± △ A B ± △ B = A ± △ A B ± △ B - 1 ⇒ Z 1 ± △ Z Z = A 1 + △ A A B - 1 1 + △ B B - 1 ⇒ 1 + ∆ Z Z = 1 + ∆ A A + ∆ B B + ∆ A ∆ B A B Since, △ A △ B are very small, so, we can neglect this term. 1 + ∆ Z Z = 1 + ∆ A A + ∆ B B ∆ Z Z = ∆ A A + ∆ B B Hence, proved.

The masses of two bodies are measured to be 15 . 7 ± 0 . 2 kg and 27 . 3 ± 0 . 3 kg . What is the total mass of the two and the error in it?

Given, The mass of the first body A , m A = 15 . 7 ± 0 . 2 kg The mass of the second body B , m B = 27 . 3 ± 0 . 3 kg Let the sum of two masses A , B be Z and their error be △ Z . The total mass of the two given body is given by, Z = A + B Z = 15 . 7 + 27 . 3 = 43 kg Hence, the total mass of the body is 43 kg . The absolute error in the result is given by, △ Z = ± △ A + △ B △ Z = ± ( 0 . 2 + 0 . 3 ) = ± 0 . 5 kg Hence, the error in the result is ± 0 . 5 kg .

The distance travelled by an object in time ( 100 ± 1 ) s is ( 5 . 2 ± 0 . 1 ) m . What is the speed and it's error?

Given, The distance traveled by the object, d = ( 5 . 2 ± 0 . 1 ) m Time, t = 100 ± 1 s We know that speed is defined as the distance traveled by an object in unit time. v = d t v = 5 . 2 100 = 0 . 052 = 5 . 2 × 10 - 2 m / s Here value is shown as per two significant figures. The maximum relative error in the speed is given by, △ v v = ± △ d d + △ t t △ v 0 . 052 = ± 0 . 1 5 . 2 + 1 100 △ v = ± 0 . 00152 = 0 . 15 × 10 - 2 m s as per two significant figures. The speed of an object is v = ( 5 . 2 ± 0 . 15 ) × 10 - 2 m / s

E M B I B E

Physics>Chapter 1 - Units and Measurements>Exercises>Q 2

EASY

11th Maharashtra Board

IMPORTANT

Earn 100

What are the dimensions of the quantity $l \sqrt{\frac{l}{g}}$ $l$ being the length and $g$ the acceleration due to gravity?

Important Questions on Units and Measurements

EASY

11th Maharashtra Board

IMPORTANT

Physics>Chapter 1 - Units and Measurements>Exercises>Q 2

Define absolute error, mean absolute error, relative error and mean percentage error.

MEDIUM

11th Maharashtra Board

IMPORTANT

Physics>Chapter 1 - Units and Measurements>Exercises>Q 2

Describe what is meant by significant figures and order of magnitude.

MEDIUM

11th Maharashtra Board

IMPORTANT

Physics>Chapter 1 - Units and Measurements>Exercises>Q 2

If the measured values of two quantities are $A \pm ∆ A a n d B \pm ∆ B$ being the mean absolute errors. What is the maximum possible error in $A \pm B$

Show that if $Z = \frac{A}{B}$

$\frac{∆ Z}{Z} = \frac{∆ A}{A} + \frac{∆ B}{B}$

HARD

11th Maharashtra Board

IMPORTANT

Physics>Chapter 1 - Units and Measurements>Exercises>Q 2

Derive the formula for kinetic energy of a particle having mass m and velocity v using dimensional analysis.

HARD

11th Maharashtra Board

IMPORTANT

Physics>Chapter 1 - Units and Measurements>Exercises>Q 3

The masses of two bodies are measured to be

15.7 \pm 0.2 kg

and

27.3 \pm 0.3 kg

. What is the total mass of the two and the error in it?

HARD

11th Maharashtra Board

IMPORTANT

Physics>Chapter 1 - Units and Measurements>Exercises>Q 3

An electron with $e$ enters a uniform magnetic field $\vec{B}$ with a velocity $\vec{v}$ . The velocity is perpendicular to the magnetic field. The force on the charge $e$ is given by $|\vec{F}|$ = $B e v$ Obtain the dimensions of $\vec{B}$ .