Physics-
General
Easy
Question
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.
- 2
- 3
- 4
- 5
The correct answer is: 4
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Physics-General
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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
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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
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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
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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
Physics-
A man having a wrist watch and a pendulum clock rises on a TV tower. The wrist watch and pendulum clock per chance fall from the top of the tower. Then
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)
A man having a wrist watch and a pendulum clock rises on a TV tower. The wrist watch and pendulum clock per chance fall from the top of the tower. Then
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)
Physics-General
Physics-
A man weighing 60 kg stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude 0.1 m and frequency
. Which of the following statement is correct
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)
A man weighing 60 kg stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude 0.1 m and frequency
. Which of the following statement is correct
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)
Physics-General
Physics-
Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiffness k is T. When block is uncharged. If a charge q is given to the block them, the new time period of oscillation will be
![](data:image/png;base64,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)
Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiffness k is T. When block is uncharged. If a charge q is given to the block them, the new time period of oscillation will be
![](data:image/png;base64,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)
Physics-General
Physics-
The period of a simple pendulum, whose bob is a hollow metallic sphere, is T. The period is T1 when the bob is filled with sand, T2 when it is filled with mercury and T3 when it is half filled with mercury. Which of the following is true
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)
The period of a simple pendulum, whose bob is a hollow metallic sphere, is T. The period is T1 when the bob is filled with sand, T2 when it is filled with mercury and T3 when it is half filled with mercury. Which of the following is true
![](data:image/png;base64,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)
Physics-General
Physics-
The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is
![](data:image/png;base64,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)
The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is
![](data:image/png;base64,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)
Physics-General