Question
Two smooth tracks of equal length have “bumps”-- A up, and B down, both of the same curvature and size. The two balls start simultaneously with the same initial speed = 3 m/s. If the speed of the ball at the bottom of the curve on track B is 4 m/s, then the speed of the ball at the top of the curve on track A is
![](data:image/png;base64,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)
- = 2 m/s
- > 2 m/s
- < 2 m/s
- not enough information given
The correct answer is: = 2 m/s
Related Questions to study
Two trolley A and B are moving with accelerations a and 2a respectively in the same direction. To an observer in trolley A, the magnitude of pseudo force acting on a block of mass m on the trolley B is
![](data:image/png;base64,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)
Two trolley A and B are moving with accelerations a and 2a respectively in the same direction. To an observer in trolley A, the magnitude of pseudo force acting on a block of mass m on the trolley B is
![](data:image/png;base64,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)
In the arrangement shown in figure. The ratio of velocity V1 & V2 of block (1) & (2) is
![](data:image/png;base64,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)
In the arrangement shown in figure. The ratio of velocity V1 & V2 of block (1) & (2) is
![](data:image/png;base64,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)
Moment of inertia of a thin uniform semicircular wire having mass M, radius R and centre C about an axis passing through point O and perpendicular to its plane is
![](data:image/png;base64,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)
Moment of inertia of a thin uniform semicircular wire having mass M, radius R and centre C about an axis passing through point O and perpendicular to its plane is
![](data:image/png;base64,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)
A uniform rod having length L, is made of material having density
, coefficient of thermal expansion
and young's modulus Y. It is placed between two vertical walls having separation L and coefficient of friction
. What is the minimum rise in temperature so that the rod does not falls down on releasing
![](data:image/png;base64,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)
A uniform rod having length L, is made of material having density
, coefficient of thermal expansion
and young's modulus Y. It is placed between two vertical walls having separation L and coefficient of friction
. What is the minimum rise in temperature so that the rod does not falls down on releasing
![](data:image/png;base64,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)
A block of mass m moving on the horizontal x-y plane having coefficient of friction
. The particle has a velocity
and acceleration
Unit vector along the direction of friction force acting on the particle is
A block of mass m moving on the horizontal x-y plane having coefficient of friction
. The particle has a velocity
and acceleration
Unit vector along the direction of friction force acting on the particle is
In wave, displacement of origin is varying according to
of disturbance is propagating in + x direction with speed 2 cm/sec, then displacement of particle at x = 4 cm at t = 5 sec. is
In wave, displacement of origin is varying according to
of disturbance is propagating in + x direction with speed 2 cm/sec, then displacement of particle at x = 4 cm at t = 5 sec. is
A point-like object of mass 2.0 kg moves along the x-axis with a velocity of + 4.0 m/s. A net horizontal force acting along the x-axis is applied to the object with the force-time profile shown. What is the total work that was done by the force?
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)
A point-like object of mass 2.0 kg moves along the x-axis with a velocity of + 4.0 m/s. A net horizontal force acting along the x-axis is applied to the object with the force-time profile shown. What is the total work that was done by the force?
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)
A mass on the end of a spring oscillates with the displacement versus time graph shown to the right. Which of the following statements about its motion is CORRECT?
![](data:image/png;base64,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)
A mass on the end of a spring oscillates with the displacement versus time graph shown to the right. Which of the following statements about its motion is CORRECT?
![](data:image/png;base64,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)
Consider the cyclic process ABCA shown in figure, performed on a sample of 1 mole of an ideal gas. A total of 1000 J of heat is withdrawn from the sample in the process, the work done on the gas during part BC is 1830 J, the value of Tb is (R = 8.3 J/K-mole)
![](data:image/png;base64,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)
Consider the cyclic process ABCA shown in figure, performed on a sample of 1 mole of an ideal gas. A total of 1000 J of heat is withdrawn from the sample in the process, the work done on the gas during part BC is 1830 J, the value of Tb is (R = 8.3 J/K-mole)
![](data:image/png;base64,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)
A rubber ball bounces on the ground as shown. After each bounce, the ball reaches one-half the highest of the bounce before it. If the time the ball was in the air between the first and second bounce was 1 second, what would be the time between the second and third bounce?
![](data:image/png;base64,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)
A rubber ball bounces on the ground as shown. After each bounce, the ball reaches one-half the highest of the bounce before it. If the time the ball was in the air between the first and second bounce was 1 second, what would be the time between the second and third bounce?
![](data:image/png;base64,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)
A monatomic ideal gas is used as the working substance for the Carnot cycle shown in the figure. Processes AB and CD are isothermal, while processes BC and DA are adiabatic. During process AB, 400 J of work is done by the gas on the surroundings. How much heat is expelled by the gas during process CD?
![](data:image/png;base64,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)
A monatomic ideal gas is used as the working substance for the Carnot cycle shown in the figure. Processes AB and CD are isothermal, while processes BC and DA are adiabatic. During process AB, 400 J of work is done by the gas on the surroundings. How much heat is expelled by the gas during process CD?
![](data:image/png;base64,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)
A projectle is fired horizontally from an inclined plane (of inclination 30° with horizontal) with speed = 50 m/s. If
, range of the projectile measured along the incline is
A projectle is fired horizontally from an inclined plane (of inclination 30° with horizontal) with speed = 50 m/s. If
, range of the projectile measured along the incline is
The two points A and B in a plane are such that for all points P lies on circle satisfied
, then k will not be equal to
So here we have given the two points A and B in a plane are such that for all points P lies on circle satisfied . We can also use equation of circle to find the answer. So here the correct option is none of these.
The two points A and B in a plane are such that for all points P lies on circle satisfied
, then k will not be equal to
So here we have given the two points A and B in a plane are such that for all points P lies on circle satisfied . We can also use equation of circle to find the answer. So here the correct option is none of these.
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius. The locus of the centre of the circle is
So here we have given to find the locus is in which form. We used the concept of circles and solved the question. We can also use equation of circle to find the answer. So the locus is x2-10y+5=0, this is the representation of parabola, so correct answer is parabola.
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius. The locus of the centre of the circle is
So here we have given to find the locus is in which form. We used the concept of circles and solved the question. We can also use equation of circle to find the answer. So the locus is x2-10y+5=0, this is the representation of parabola, so correct answer is parabola.
If d is the distance between the centres of two circles,
are their radii and
, then
For such questions, we have to see how the cricles are with respect to each other to find the distance between the centers.
If d is the distance between the centres of two circles,
are their radii and
, then
For such questions, we have to see how the cricles are with respect to each other to find the distance between the centers.