Question
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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)
- The frequency of oscillations is 2 Hz
- The mass achieves a maximum speed at t = 1.5 second.
- The mass experiences a maximum acceleration at t = 1 sec.
- All are incorrect.
The correct answer is: All are incorrect.
Related Questions to study
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 A total of 1000 J of heat is withdrawn from the sample in the process, the work done on the gas during part BC is 1830 J, the value of Tb is (R = 8.3 J/K-mole)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 A total of 1000 J of heat is withdrawn from the sample in the process, the work done on the gas during part BC is 1830 J, the value of Tb is (R = 8.3 J/K-mole)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.