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

Find the Dimensions of Planck'S Constant H From the Equation E = Hv Where E Is the Energy And V is the Frequency.

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

E = hv, where E is the energy and v is the frequency

\[\text{ Here,} \left[ E \right] = {\left[ {ML}^2 T^{- 2} \right]}\text{ and }{\left[ v \right]} = {\left[ T^{- 1} \right]}\]

\[\text{ So, }\left[ h \right] = \frac{\left[ E \right]}{\left[ v \right]} = \frac{\left[ {ML}^2 T^{- 2} \right]}{\left[ T^{- 1} \right]} = \left[ {ML}^2 T^{- 1} \right]\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Introduction to Physics - Exercise [पृष्ठ १०]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 1 Introduction to Physics
Exercise | Q 5 | पृष्ठ १०

संबंधित प्रश्न

Suggest a way to measure the thickness of a sheet of paper.


A unitless quantity


Find the dimensions of magnetic field B.
The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]

where F is force, q is charge, v is speed, I is current, and a is distance.


Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are \[{\text{ML}}^2 \text{I}^{- 2} \text{T}^{- 3}\] and \[{\text{ML}}^2 \text{T}^{- 3} \text{I}^{- 1}\] respectively.


Test if the following equation is dimensionally correct:
\[v = \frac{1}{2 \pi}\sqrt{\frac{mgl}{I}};\] 
where h = height, S = surface tension, \[\rho\] = density, P = pressure, V = volume, \[\eta =\] coefficient of viscosity, v = frequency and I = moment of interia.


Is a vector necessarily changed if it is rotated through an angle?


Is the vector sum of the unit vectors  \[\vec{i}\] and \[\vec{i}\] a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?

 


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


Which of the sets given below may represent the magnitudes of three vectors adding to zero?


The resultant of  \[\vec{A} \text { and } \vec{B}\] makes an angle α with  \[\vec{A}\] and β with \[\vec{B}\],


A vector \[\vec{A}\] points vertically upward and \[\vec{B}\] points towards the north. The vector product \[\vec{A} \times \vec{B}\] is


Let the angle between two nonzero vectors \[\vec{A}\] and \[\vec{B}\] be 120° and its resultant be \[\vec{C}\].


The x-component of the resultant of several vectors
(a) is equal to the sum of the x-components of the vectors of the vectors
(b) may be smaller than the sum of the magnitudes of the vectors
(c) may be greater than the sum of the magnitudes of the vectors
(d) may be equal to the sum of the magnitudes of the vectors.


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 \[\overrightarrow{OA}, \overrightarrow{BC} \text { and } \overrightarrow{DE}\].


Two vectors have magnitudes 2 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.


Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
cos 0 + cos π/3 + cos 2π/3 + cos 3π/3 + cos 4π/3 + cos 5π/3 = 0.
Use the known cosine values to verify the result.


If  \[\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}\] find \[\vec{A} \times \vec{B}\].


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 \[\tan \theta = \frac{dy}{dx} = 4x\] 
\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]


If π = 3.14, then the value of π2 is ______


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×