Physics
General
Easy
Question
Two masses M and M/2 are joined to gether by means of light inexcusable string passed aver Z, fiction pulley as shown in fig. When the bigger mass is rekasod, the small and will ascend with an acceleration
![](data:image/png;base64,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)
- g/3
![fraction numerator 3 g over denominator 2 end fraction](data:image/png;base64,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)
- g
- g/2
The correct answer is: g/3
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physics
A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below The velocity of the particle after 10s is
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)
A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below The velocity of the particle after 10s is
![](data:image/png;base64,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)
physicsGeneral
physics-
For the figure
![](data:image/png;base64,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)
For the figure
![](data:image/png;base64,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)
physics-General
physics
A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity
Here is the time in second. All surfaces are smooth. The sphere is at rest with respect to the cube. what is the total force exerted by the sphere on the cube(g=10ms-2)
![](data:image/png;base64,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)
A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity
Here is the time in second. All surfaces are smooth. The sphere is at rest with respect to the cube. what is the total force exerted by the sphere on the cube(g=10ms-2)
![](data:image/png;base64,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)
physicsGeneral
physics-
A projectile A is the thrown at an angle of
to the horizontal from point P. At the same time, another projectile B is thrown with velocity
upwards from the point Q vertically below the highest point. For B to collide with A,
should be-
![](data:image/png;base64,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)
A projectile A is the thrown at an angle of
to the horizontal from point P. At the same time, another projectile B is thrown with velocity
upwards from the point Q vertically below the highest point. For B to collide with A,
should be-
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about P?
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)
A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about P?
![](data:image/png;base64,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)
physics-General
physics-
Two forces each numerically equal to 10 dynes are acting as shown in the following figure, then the resultant is –
![](data:image/png;base64,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)
Two forces each numerically equal to 10 dynes are acting as shown in the following figure, then the resultant is –
![](data:image/png;base64,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)
physics-General
physics
Three Forces F1 and F2 together keep a body in equillibrcium. If F1 =3 N along the positive X axis F2 =4 N along the positive Y. axis, then the third force F3 is
Three Forces F1 and F2 together keep a body in equillibrcium. If F1 =3 N along the positive X axis F2 =4 N along the positive Y. axis, then the third force F3 is
physicsGeneral
physics-
A boat moving upstream with velocity 3
w.r.t. ground. An observer standing on boat observes that swimmer 'S' is crossing the river perpendicular to the direction of motion of boat. If river velocity is 4m/s & swimmer crosses the river width 100 m in 50 sec then -
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/485436/1/896783/Picture148.png)
A boat moving upstream with velocity 3
w.r.t. ground. An observer standing on boat observes that swimmer 'S' is crossing the river perpendicular to the direction of motion of boat. If river velocity is 4m/s & swimmer crosses the river width 100 m in 50 sec then -
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/485436/1/896783/Picture148.png)
physics-General
physics-
Vector
in figure represents –
![](data:image/png;base64,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)
Vector
in figure represents –
![](data:image/png;base64,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)
physics-General