Answer
427.8k+ views
Hint: The pendulum is in a rest position. All the forces i.e. components of force and the other force will be in balanced state. When we equate the horizontal and vertical forces, we can find the tension in the thread of a string.
Step by step answer: A pendulum bob is at a rest position in a uniform horizontal electric field E = 20000 Vm-1.. The mass m of bob is 80 mg i.e., 80 × 10-3 kg (1g =10-3kg) is carrying a charge q = 2 × 10⁻⁸ C and let the tension in the thread of the string be T and the angle made by the string with vertical be Ɵ. As the pendulum bob is in a rest position i.e. in equilibrium. So, all the forces acting on the bob will be in a balanced state.
$T\sin \theta = qE$ [T sin Ɵ is the component of T acting horizontally which balances the force acted due to electric field]
$T\cos \theta = mg$ [T cos Ɵ is the component of T acting vertically upwards which is balanced by the weight of the body mg]
When we divide the above two equations,
$\dfrac{{T\sin \theta }}{{T\cos \theta }} = \dfrac{{qE}}{{mg}}$
$\Rightarrow$ $\tan \theta = \dfrac{{qE}}{{mg}}\left[ {\tan \theta = \dfrac{{\sin \theta }}{{\cos \theta }}} \right]$
$\Rightarrow$ \[\tan \theta = \dfrac{{2 \times {{10}^{ - 5}} \times 20000}}{{80 \times {{10}^{ - 3}} \times 10}}\]
$\Rightarrow$ $\tan \theta = 0.5$
$\Rightarrow$ ${\tan ^{ - 1}}\left( {0.5} \right)$
$\Rightarrow$ $\theta = 27\left[ {{{\tan }^{ - 1}}\left( {0.5} \right) = 26.5} \right]$
Now, from the first equation ,
$
T\sin \theta = qE \\
\Rightarrow T = \dfrac{{qE}}{{\sin \theta }} \\
\Rightarrow T = \dfrac{{2 \times {{10}^{ - 5}} \times 20000}}{{0.453}} \\
\Rightarrow T = 88300.22 \times {10^{ - 8}} \\
$\therefore$ T = 8.8 \times {10^{ - 4}} \\
$
Therefore, option C is correct.
Note: The electric field acts in a horizontal direction which balances the horizontal component of force and the weight of the bob balances the vertical component of force. In equilibrium, all the forces are in a balanced state.
Step by step answer: A pendulum bob is at a rest position in a uniform horizontal electric field E = 20000 Vm-1.. The mass m of bob is 80 mg i.e., 80 × 10-3 kg (1g =10-3kg) is carrying a charge q = 2 × 10⁻⁸ C and let the tension in the thread of the string be T and the angle made by the string with vertical be Ɵ. As the pendulum bob is in a rest position i.e. in equilibrium. So, all the forces acting on the bob will be in a balanced state.
$T\sin \theta = qE$ [T sin Ɵ is the component of T acting horizontally which balances the force acted due to electric field]
$T\cos \theta = mg$ [T cos Ɵ is the component of T acting vertically upwards which is balanced by the weight of the body mg]
When we divide the above two equations,
$\dfrac{{T\sin \theta }}{{T\cos \theta }} = \dfrac{{qE}}{{mg}}$
$\Rightarrow$ $\tan \theta = \dfrac{{qE}}{{mg}}\left[ {\tan \theta = \dfrac{{\sin \theta }}{{\cos \theta }}} \right]$
$\Rightarrow$ \[\tan \theta = \dfrac{{2 \times {{10}^{ - 5}} \times 20000}}{{80 \times {{10}^{ - 3}} \times 10}}\]
$\Rightarrow$ $\tan \theta = 0.5$
$\Rightarrow$ ${\tan ^{ - 1}}\left( {0.5} \right)$
$\Rightarrow$ $\theta = 27\left[ {{{\tan }^{ - 1}}\left( {0.5} \right) = 26.5} \right]$
Now, from the first equation ,
$
T\sin \theta = qE \\
\Rightarrow T = \dfrac{{qE}}{{\sin \theta }} \\
\Rightarrow T = \dfrac{{2 \times {{10}^{ - 5}} \times 20000}}{{0.453}} \\
\Rightarrow T = 88300.22 \times {10^{ - 8}} \\
$\therefore$ T = 8.8 \times {10^{ - 4}} \\
$
Therefore, option C is correct.
Note: The electric field acts in a horizontal direction which balances the horizontal component of force and the weight of the bob balances the vertical component of force. In equilibrium, all the forces are in a balanced state.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)