Physics-
General
Easy
Question
The equation
represents a wave with
- Amplitude A/2, frequency
and wavelength
- Amplitude A/2, frequency
and wavelength
- Amplitude A, frequency
and wavelength
- Amplitude A, frequency
and wavelength
The correct answer is: Amplitude A/2, frequency
and wavelength ![lambda divided by 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAPCAYAAAAceBSiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAPtJREFUeNpjYKAOMADiowwDBGYDcTQlBjAB8S0gtiVRnygQ34fqRwbWQLwGiD8B8S8gvkDIgSxAvBSIhUmwvBqIa7GIHwTiSCDmgfK1oFETic8wDxyG4Qqt+1DfEwPkgfgSIQPPEWkYyBdzSYymH4QUHCUy7g8DsTEJFlsSyhUZQFxChI9IzV4cQHwSmhCxAhUg3oCUYHiolL0Eoea64Yvr3UAsjpSK00jMXtiAEtRiFXyKmtGygTE0TknJXuhAAxpCXIQSwhos4vex5HlisxcoBFdByw6cgAeaELAVLF1Ygp7Y7LUF6nO8YCEQB+GQ0wPi42Rmr/948MADAJRGM96VahREAAAAY3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT4mI3gzQkI7PC9taT48bW8+LzwvbW8+PG1uPjI8L21uPjwvbWF0aD7uxhqOAAAAAElFTkSuQmCC)
The given equation can be x written as
![y equals fraction numerator A over denominator 2 end fraction cos invisible function application open parentheses 4 pi n t minus fraction numerator 4 pi x over denominator lambda end fraction close parentheses plus fraction numerator A over denominator 2 end fraction blank open parentheses because cos to the power of 2 end exponent invisible function application theta equals fraction numerator 1 plus cos invisible function application 2 theta over denominator 2 end fraction close parentheses](data:image/png;base64,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)
Hence amplitude
and frequency ![equals fraction numerator omega over denominator 2 pi end fraction equals fraction numerator 4 pi n over denominator 2 pi end fraction equals 2 n](data:image/png;base64,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)
and wave length ![equals fraction numerator 2 pi over denominator k end fraction equals fraction numerator 2 pi over denominator 4 pi divided by lambda end fraction equals fraction numerator lambda over denominator 2 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAAAjCAYAAABoz8OXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAxhJREFUeNrtWzFrVEEQXg6RQ64JEsQiBOQKkRCEIBIkhY2IpAhpRFKJICKWgkUIFiKIWIkIIiEEkUAQEUkXJIgcIU0QCwtB/AcWIiHYJN+Qefh8vtvbveRlZ9/OBx9kL1fM7M3uzJs3nzHV4QL4BvwF/gE/gzOmnkjJ1wb4DZwIbchH8BrY4vUZsMOf1Q0p+Uo4Ar4Gj0szbBj8YtJA3X29DM5JNGy7y+e3wS1wx8J7kf0IdfaVUuWmNKPGOXWUYREc4lpmKvc5rScjPOEp+NqRUItlaIIbXBDb8J03P8MP8ERkwZWCr7fAu+C8BGMGwHfgJYficauw/h1ZcKXga5t9zB5wWiGNOcXGtB3Tylph/SGi4ErBV6q9VnM37Sx4M5Qxp8GX4DHH79Nj/UJufZXrlRiQiq8PzL/tlzHwUwhDKMKX+ep3xXPwesGZZxFseiq+jvODSBFUOx56T2yFT7UPqOg9m1s/5Ou47XEzhEAKvrb4waUskB6HSJO2Hk8Zpkr6KufM3uuXV8JPdgq+Uvqe7vK/UXDdKBQKhUKhqKqesNUVar/uiUJR/5NyUIzd/rrviaZIPfiaIhUKhUIRC+jVUUe3QVEVaBpjRrfh4EADd41IbJ2suBgeNHtTCWX7IUUqFpU8j6YGYlHd0CTB14oDjAb3bCodCVKxqOR5NFGwFEmAvQBvVBhgDb69Bnt8T6JUTKw87775K82i00njIFcE2klpIRtltgXYfqRodAPMOwbipsA92pYYYMt8izX574sCbTzKp3PYIcD2I0WjkeMxR5tEScWMXZ4XFFS0joDvwfNCU+Mj8E5u7ZIifaVoPq0JUVIx4y7PO3Q0OJ2sc5BJxGjJD98rwPqRorm2JkRJxYy7PC8I6MZa86g9QmDD/C8/6xVgvlI0W2uieCDFSMWMnzwvCPKSrSd89UtDPy+HfaVovVoTGcRIxYy/PC8InhZO4KrEPN4l6GzwkaK5tiYkScX6kecFwdtCS2KAU9LJyAPMR4rmUh5Ik4r1I88Lgp/8BJLHCNcrzUgDzFeK5tKakCYV854n2wVB1Hyk24aJdwAAAT10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtbj4yPC9tbj48bWk+JiN4M0MwOzwvbWk+PC9tcm93PjxtaT5rPC9taT48L21mcmFjPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1uPjI8L21uPjxtaT4mI3gzQzA7PC9taT48L21yb3c+PG1yb3c+PG1uPjQ8L21uPjxtaT4mI3gzQzA7PC9taT48bW8+LzwvbW8+PG1pPiYjeDNCQjs8L21pPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWZyYWM+PG1pPiYjeDNCQjs8L21pPjxtbj4yPC9tbj48L21mcmFjPjwvbWF0aD4v37OIAAAAAElFTkSuQmCC)
Related Questions to study
Physics-
A train has just complicated a U-curve in a track which is a semicircle. The engine is at the forward end of the semi circular part of the track while the last carriage is at the rear end of the semicircular track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is 340 m/sec. Then the apparent frequency as observed by a passenger in the middle of a train when the speed of the train is 30 m/sec is
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)
A train has just complicated a U-curve in a track which is a semicircle. The engine is at the forward end of the semi circular part of the track while the last carriage is at the rear end of the semicircular track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is 340 m/sec. Then the apparent frequency as observed by a passenger in the middle of a train when the speed of the train is 30 m/sec is
![](data:image/png;base64,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)
Physics-General
Physics-
Two vectors
and
will be parallel if
Two vectors
and
will be parallel if
Physics-General
Physics-
A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is ![left parenthesis angle P O Q equals 40 degree right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is ![left parenthesis angle P O Q equals 40 degree right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGcAAAAQCAYAAAALZmGAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAx1JREFUeNrtWVFkW1EYvmKipkZMH2aqTM3sIUJNVeyhTMzUzJjaw8yMmIjZQ5mZ2sOUij3UHkZMVFWVitlD1aiaqYiyh6ma2cvMHqbGVFVEjOz/+cLJv3PuOffmJhP68ZHc++ee/5zvP///nxvPa0eOOO8d439gHuuvRZJYjWigq8dr7QsW4Yh4KASpQId/wDdSEQz8krgqrtWJTZCdWiNOGgKkRNyH40vEiz5jZYjviDWMsW14btSYwlx0OEV8RdwBi7imguc2TDyHzy2MYQ5tSEGcTsAObBC/EkeU66PET8r3OPEK8ZtY+FniW+IlYgy8QfxOHDekAWl/HcKmuyjMIPGzjzhb8EMVckvYHGFdRoQ4HsQZUy8UiPkOHB6Gw+xEQtzjBV7R/OY+cQafnyLCdJgU4jIeWuyrXRSnCN914txC5pBYIN5WvmeJBxAmq5lbW93n1HA5pLNpRGsJ0SvxTBFBRj4HxHniF8Nv1TSQUAJhz2J/gB0aNdLKLtCJU0aq1QVM2XGMCbnTDkNO5g5y/YyPzZrY5owhpL/TxBcOu3ZTCZ45R3td/Ww60ARen10lZetsfxvWMY4AdkFcpro/IVu/mmbhJViEM6LoVZTCvSdqlA4/lKLqYs916mQXWt28EFrCbx0bAcZqhBVnEIX4pyxcGsTw7CaiikV5rogVg8B+OIE0FcY+KiQ1DVNQcephxXFNa2dRnHfFbjCBu6z3QbawocguKwtvs7+JFtyLMK3toLuyibNvWMeBTtLapkP7OY4BNrB7XMAdyqJlZzUsxb0iWumag30q4p3jKmjZcADPdNIQ2FrpaWzLhRAH0qzFZp14z3DviaZlXrLYF3p0ym8adu1rzfVF0Ur7IS/n4HcInYUjuRATeEO8ZrEZRSt9F2mr5c+y4SxzAQ2Cap+E/VwPX8GYUiCn8UfwLY4z3IcAz93W1fKq5r3OqmOebnFd01oOOB5iS7D/hUPrhEMtqyuvhnJeb2ESJ4G51JGCiwHKgPb1TSv6ql5/Yhrd40ec3of6dB7GF5+MB17//mXA0fkYr5Eyfeh/Qdbnv1RV5AlniKXZAAAApnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bWk+JiN4MjIyMDs8L21pPjxtaT5QPC9taT48bWk+TzwvbWk+PG1pPlE8L21pPjxtbz49PC9tbz48bW4+NDA8L21uPjxtbz4mI3hCMDs8L21vPjxtbz4pPC9tbz48L21hdGg+T8fyyAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Physics-General
Physics-
Figure below shows a body of mass M moving with the uniform speed on a circular path of radius, R. What is the change in acceleration in going from
to ![P subscript 2 end subscript](data:image/png;base64,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)
![](data:image/png;base64,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)
Figure below shows a body of mass M moving with the uniform speed on a circular path of radius, R. What is the change in acceleration in going from
to ![P subscript 2 end subscript](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAARCAYAAADQWvz5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAL9JREFUeNpjYMAEP4D4PxR/AeJVQOzIQCJQAeILSHw2IHYB4vtArEWKQQFAvBSLeDIQl5BiUD0ODR1AnEOKQaDw8EMTEwXiW0AsTIpBIA2SSHxjID5KamAzAfEfaGy9gxrQjGYwUcAciPczUAFEAvF8Ampg6esX1MUq2BRNAuI0EoIhC4jPYZNcB8ReJPriBzZBUABzkGCIPRAfpDQ8JaFhpESJIWpAvIWcZIHukm1AzEepl0CGaFAjrf3HgsEAACEtJ9L53V4ZAAAAYHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3ViPjxtaT5QPC9taT48bW4+MjwvbW4+PC9tc3ViPjwvbWF0aD7r1BiOAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Physics-General
Physics-
A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong
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)
A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong
![](data:image/png;base64,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)
Physics-General
Physics-
The length of second's hand in watch is 1 cm. The change in velocity of its tip in 15 seconds is
The length of second's hand in watch is 1 cm. The change in velocity of its tip in 15 seconds is
Physics-General
Physics-
Figure shows ABCDEF as a regular hexagon. What is the value of ![Error converting from MathML to accessible text.](data:image/png;base64,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)
![](data:image/png;base64,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)
Figure shows ABCDEF as a regular hexagon. What is the value of ![Error converting from MathML to accessible text.](data:image/png;base64,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)
![](data:image/png;base64,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)
Physics-General
Physics-
Find the resultant of three vectors
and
shown in the following figure. Radius of the circle is R.
![](data:image/png;base64,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)
Find the resultant of three vectors
and
shown in the following figure. Radius of the circle is R.
![](data:image/png;base64,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)
Physics-General
Physics-
From the equation
, one can obtain the angle of banking
for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is
From the equation
, one can obtain the angle of banking
for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is
Physics-General
Physics-
Number of particles is given by
crossing a unit area perpendicular to X-axis in unit time, where
and
are number of particles per unit volume for the value of
meant to
and
. Find dimensions of
called as diffusion constant
Number of particles is given by
crossing a unit area perpendicular to X-axis in unit time, where
and
are number of particles per unit volume for the value of
meant to
and
. Find dimensions of
called as diffusion constant
Physics-General
Physics-
A thin uniform rod AB of length L and mass M hangs from a smooth pivot at A and is connected at the bottom by a spring of constant K to wall as shown. The system is set into oscillation by slightly displacing end B. The period of oscillation is
![](data:image/png;base64,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)
A thin uniform rod AB of length L and mass M hangs from a smooth pivot at A and is connected at the bottom by a spring of constant K to wall as shown. The system is set into oscillation by slightly displacing end B. The period of oscillation is
![](data:image/png;base64,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)
Physics-General
Physics-
The displacement of a particle from its mean position (in metre) is given by
. The motion of particle is
The displacement of a particle from its mean position (in metre) is given by
. The motion of particle is
Physics-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
![](data:image/png;base64,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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
![](data:image/png;base64,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)
Physics-General