Physics-
General
Easy
Question
A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity
. The induced e.m.f. between the two ends is
The correct answer is: ![fraction numerator 1 over denominator 2 end fraction B omega l to the power of 2 end exponent](data:image/png;base64,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)
If in time t. the rod turns by an angle q, the area generated by the rotation of rod will be ![equals fraction numerator 1 over denominator 2 end fraction l cross times l theta equals fraction numerator 1 over denominator 2 end fraction l to the power of 2 end exponent theta](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/860566/1/1167884/Picture555.png)
So the flux linked with the area generated by the rotation of rod
![phi equals B open parentheses fraction numerator 1 over denominator 2 end fraction l to the power of 2 end exponent theta close parentheses cos invisible function application 0 equals fraction numerator 1 over denominator 2 end fraction B l to the power of 2 end exponent theta equals fraction numerator 1 over denominator 2 end fraction B l to the power of 2 end exponent omega t](data:image/png;base64,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)
And so ![e equals fraction numerator d phi over denominator d t end fraction equals fraction numerator d over denominator d t end fraction open parentheses fraction numerator 1 over denominator 2 end fraction B l to the power of 2 end exponent omega t close parentheses equals fraction numerator 1 over denominator 2 end fraction B l to the power of 2 end exponent omega](data:image/png;base64,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)
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In the figure shown a particle of mass m moving with velocity
strike a wall ( mass is infinitely large) moving towards the particle with same speed The work done on the particle during collision is
![](data:image/png;base64,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)
In the figure shown a particle of mass m moving with velocity
strike a wall ( mass is infinitely large) moving towards the particle with same speed The work done on the particle during collision is
![](data:image/png;base64,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)
Physics-General
Physics-
A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The centre of the smaller circle is at a distance of R/3 from the centre of the larger circle. What is the position of the centre of man of the plate
A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The centre of the smaller circle is at a distance of R/3 from the centre of the larger circle. What is the position of the centre of man of the plate
Physics-General
Physics-
The kinetic energy of a body decreases by 36%. The decrease in its momentum is
The kinetic energy of a body decreases by 36%. The decrease in its momentum is
Physics-General
Physics-
A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x ?
A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x ?
Physics-General
Physics-
Which of the following graphs is correct between kinetic energy (E), potential energy (U) and height (h) from the ground of the particle
Which of the following graphs is correct between kinetic energy (E), potential energy (U) and height (h) from the ground of the particle
Physics-General
Chemistry-
When pH of a solution is 2, the hydrogen ion concentration in mol litre1 is:
When pH of a solution is 2, the hydrogen ion concentration in mol litre1 is:
Chemistry-General
Chemistry-
The decreasing order of strength of following bases is:
The decreasing order of strength of following bases is:
Chemistry-General
Physics-
Two rods ofsamelengthandareaofcross-sectionA1and A2havetheirendsatthesametemperature.If K1and K2 are their thermal conductivities,c1 and c2 are their specific heatsandd1andd2aretheirdensities,thentherateofflow of heat is the same in both the rods if
Two rods ofsamelengthandareaofcross-sectionA1and A2havetheirendsatthesametemperature.If K1and K2 are their thermal conductivities,c1 and c2 are their specific heatsandd1andd2aretheirdensities,thentherateofflow of heat is the same in both the rods if
Physics-General
Physics-
In a room where the temperature is 30
C,a body cools from 61
C to 59C in 4 minutes. The time (in minutes)taken by the body to cool from 51
c to 49
Cwill be:
In a room where the temperature is 30
C,a body cools from 61
C to 59C in 4 minutes. The time (in minutes)taken by the body to cool from 51
c to 49
Cwill be:
Physics-General
Physics-
Steam at 100
C is passed in to 20gofwateratl0
C.When water acquires a temperature of 80
C, the mass of water present will be:
Steam at 100
C is passed in to 20gofwateratl0
C.When water acquires a temperature of 80
C, the mass of water present will be:
Physics-General
Physics-
If![alpha comma beta text end text a n d](data:image/png;base64,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)
are efficient of linear, area and volume expansion respectively, then
If![alpha comma beta text end text a n d](data:image/png;base64,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)
are efficient of linear, area and volume expansion respectively, then
Physics-General
Physics-
Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minute and for smaller one is 16 minute, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is
Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minute and for smaller one is 16 minute, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is
Physics-General
Physics-
A long metallicbar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature 0 along the length x of the bar from its hot end is best described by which of the following figures?
A long metallicbar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature 0 along the length x of the bar from its hot end is best described by which of the following figures?
Physics-General
Physics-
Two rods of same length and transfer a given amount of heat12second,whentheyarejoined as shown in figure (i).But when they are joined as shown in figure (ii), then they will transfer same heat in same
conditions in
![](data:image/png;base64,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)
Two rods of same length and transfer a given amount of heat12second,whentheyarejoined as shown in figure (i).But when they are joined as shown in figure (ii), then they will transfer same heat in same
conditions in
![](data:image/png;base64,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)
Physics-General