हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

What Are the Dimensions of Volume of a Sphere of Radius A? - Physics

Advertisements
Advertisements

प्रश्न

What are the dimensions of volume of a sphere of radius a?

टिप्पणी लिखिए
Advertisements

उत्तर

Volume of a sphere of radius a, V =` 4/3 pi ( a )^3`
i.e [ V ] = L × L × L = L3

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Introduction to Physics - Short Answers [पृष्ठ ८]

APPEARS IN

एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
अध्याय 1 Introduction to Physics
Short Answers | Q 2.2 | पृष्ठ ८

संबंधित प्रश्न

If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?


The dimensions ML−1 T−2 may correspond to


Choose the correct statements(s):


Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque τ and
(d) moment of interia I.
Some of the equations involving these quantities are \[\omega = \frac{\theta_2 - \theta_1}{t_2 - t_1}, \alpha = \frac{\omega_2 - \omega_1}{t_2 - t_1}, \tau = F . r \text{ and }I = m r^2\].
The symbols have standard meanings.


Find the dimensions of Planck's constant h from the equation E = hv where E is the energy and v is the frequency.


Test if the following equation is dimensionally correct:
\[v = \sqrt{\frac{P}{\rho}},\]

where v = velocity, ρ = density, P = pressure


Test if the following equation is dimensionally correct:
\[V = \frac{\pi P r^4 t}{8 \eta l}\]

where v = frequency, P = pressure, η = coefficient of viscosity.


Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?


Can a vector have zero component along a line and still have nonzero magnitude?


Let ε1 and ε2 be the angles made by  \[\vec{A}\] and -\[\vec{A}\] with the positive X-axis. Show that tan ε1 = tan ε2. Thus, giving tan ε does not uniquely determine the direction of \[\vec{A}\].

  

Let \[\vec{A} = 5 \vec{i} - 4 \vec{j} \text { and } \vec{B} = - 7 \cdot 5 \vec{i} + 6 \vec{j}\]. Do we have \[\vec{B} = k \vec{A}\] ? Can we say \[\frac{\vec{B}}{\vec{A}}\] = k ?


A vector is not changed if


Let \[\vec{C} = \vec{A} + \vec{B}\]


The magnitude of the vector product of two vectors \[\left| \vec{A} \right|\] and \[\left| \vec{B} \right|\] may be

(a) greater than AB
(b) equal to AB
(c) less than AB
(d) equal to zero.


Let \[\vec{A} \text { and } \vec{B}\] be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angle 30° and 60° respectively, find the resultant.


Refer to figure (2 − E1). Find (a) the magnitude, (b) x and y component and (c) the angle with the X-axis of the resultant of \[\overrightarrow{OA}, \overrightarrow{BC} \text { and } \overrightarrow{DE}\].


Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?


Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].


Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve draw is y = 2x2 and the slope of tangent is \[\tan \theta = \frac{dy}{dx} = 4x\] 
\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×