Physics-
General
Easy
Question
An isolated and charged spherical soap bubble has aradiusr and the pressure in side is atmospheric. T is the surface
tension of soap solution. If charge on drop is X
the n find the value of X.
- 8
- 9
- 7
- 2
The correct answer is: 8
Related Questions to study
Physics-
Two mercury drops (each of radius 'r') merge to form bigger drop. The surface energy of the bigger drop, if T is the surface tension ,is:
Two mercury drops (each of radius 'r') merge to form bigger drop. The surface energy of the bigger drop, if T is the surface tension ,is:
Physics-General
Physics-
A thick rope of density p and length L is hung from a rigid support. The Young's modulus of the material of rope is Y. The in crease in length of the rope due to it sown weigh tis
A thick rope of density p and length L is hung from a rigid support. The Young's modulus of the material of rope is Y. The in crease in length of the rope due to it sown weigh tis
Physics-General
Physics-
Copper of fixed volume 'V; is drawn into wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is '
'. Which of the following graphs is a straight line?
Copper of fixed volume 'V; is drawn into wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is '
'. Which of the following graphs is a straight line?
Physics-General
Physics-
The change in the value of 'g'at a height 'h' a bove the surface of the earth is the same as at a depth 'd' below the surface of earth. When both 'd' and 'h' are much smallerthantheradiusofearth,thenwhichoneofthefollowingiscorrect?
The change in the value of 'g'at a height 'h' a bove the surface of the earth is the same as at a depth 'd' below the surface of earth. When both 'd' and 'h' are much smallerthantheradiusofearth,thenwhichoneofthefollowingiscorrect?
Physics-General
Physics-
The moment of inertia of a uniform semicircular wire of mass mand radiusr, about an ax is passing through it scent re of
mass and perpendicular to its plane is mr2
Find the value of k.
The moment of inertia of a uniform semicircular wire of mass mand radiusr, about an ax is passing through it scent re of
mass and perpendicular to its plane is mr2
Find the value of k.
Physics-General
Physics-
A couple produces
A couple produces
Physics-General
Physics-
A3kg balls trikes a heavy rigid wall with a speed of 10m/s at an angle of 60°.It get s reflected withthesamespeedandangleasshownhere.Iftheballisincontactwiththewallfor0.20s,whatis the average for ce exerted on the ball by the wall?
A3kg balls trikes a heavy rigid wall with a speed of 10m/s at an angle of 60°.It get s reflected withthesamespeedandangleasshownhere.Iftheballisincontactwiththewallfor0.20s,whatis the average for ce exerted on the ball by the wall?
Physics-General
Physics-
A block of mass m rests on a rough horizontal surface(Coefficient of friction isµ).When a bullet of mass ml2strikeshorizontally,andgetembeddedinit,theblockmoves a distanced before coming torest .The initialvelo city of the bulle is,
then the value of k is
![](data:image/png;base64,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)
A block of mass m rests on a rough horizontal surface(Coefficient of friction isµ).When a bullet of mass ml2strikeshorizontally,andgetembeddedinit,theblockmoves a distanced before coming torest .The initialvelo city of the bulle is,
then the value of k is
![](data:image/png;base64,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)
Physics-General
Physics-
Aspring of spring constant 5x103N/m is stretch edinitially by 5cm from theunstretchedposition.Thentheworkrequiredtostretchitfurtherbyanother5cmis
Aspring of spring constant 5x103N/m is stretch edinitially by 5cm from theunstretchedposition.Thentheworkrequiredtostretchitfurtherbyanother5cmis
Physics-General
Physics-
Two blocks are connected over a massless pulley as shown in fig. The mass of block A is 10 kg and the coefficien to f kineticfriction is 0.2.BlockA slides down the incline at constant speed. The mass of block B in kg is
![](data:image/png;base64,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)
Two blocks are connected over a massless pulley as shown in fig. The mass of block A is 10 kg and the coefficien to f kineticfriction is 0.2.BlockA slides down the incline at constant speed. The mass of block B in kg is
![](data:image/png;base64,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)
Physics-General
Physics-
Asatellite in a force frees paces weeps stationary interplanetary dust at a rate
The acceleration of satellite is
Asatellite in a force frees paces weeps stationary interplanetary dust at a rate
The acceleration of satellite is
Physics-General
Physics-
A vector of magnitude b is rotated through angle
What is the change in magnitude of the vector?
A vector of magnitude b is rotated through angle
What is the change in magnitude of the vector?
Physics-General
Physics-
Six
vectors,havethemagnitudesanddirectionsindicatedinthefigure.Whichofthefollowing
![](data:image/png;base64,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)
Six
vectors,havethemagnitudesanddirectionsindicatedinthefigure.Whichofthefollowing
![](data:image/png;base64,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)
Physics-General
Maths-
If
is defined by ![f open parentheses x close parentheses equals fraction numerator 1 minus x over denominator 1 plus x end fraction blank t h e n blank open parentheses f o blank f o blank f o f close parentheses open parentheses x close parentheses equals](data:image/png;base64,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)
If
is defined by ![f open parentheses x close parentheses equals fraction numerator 1 minus x over denominator 1 plus x end fraction blank t h e n blank open parentheses f o blank f o blank f o f close parentheses open parentheses x close parentheses equals](data:image/png;base64,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)
Maths-General
Physics-
Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction, then the frequency of oscillation of the system is
![](data:image/png;base64,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)
Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction, then the frequency of oscillation of the system is
![](data:image/png;base64,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)
Physics-General