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A parallel beam of light ray parallel to the X-axis is incident on a parabolic reflecting surface x=2by^2 as shown in the figure. After reflecting it passes through focal point F. What is the focal length of the reflecting surface?

Solution: \(\begin{array}{l}y^{2}=4ax \end{array} \) for a parabolic curve Where, a=focal length \(\begin{array}{l}y^{2}-\frac{1}{2b}\end{array} \) \(\begin{array}{l}4a=\frac{1}{2b}\end{array} \) \(\begin{array}{l}a=\frac{1}{8b}\end{array} \)

A particle executing SHM has a maximum speed of 30cms−1 and a maximum acceleration of 60cms−2 . What is the period of oscillation?

Solution: Maximum velocity \(\begin{array}{l}V_{max}=Aw=30 cm s^{-1}\end{array} \) Maximum acceleration \(\begin{array}{l}a_{max}=A^{2}w=60 cm s^{-1}\end{array} \) \(\begin{array}{l}A^{2}w=60\end{array} \) \(\begin{array}{l}A*30=60\end{array} \) A=2 cms w=30/2... View Article

A thin rod of mass m and length 2l is made to rotate about an axis passing through its centre and perpendicular to it. Its angular velocity changes from 0 to ω in time t. What is the torque acting on the rod?

Solution: Since l=2l Inertia of the rod is given by, \(\begin{array}{l}=\frac{Ml^{2}}{12}\end{array} \) From the equation of angular motion, \(\begin{array}{l}\omega _{f}=\omega... View Article

If all linear dimensions of an inductor are tripled, then self inductance will become (keeping total number of turns per unit length constant).

a) 2 times b) 3 times c) 9 times d) 27 times Solution: d) 27 times Explanation: when l is... View Article

When slightly different weights are placed on the two pans of a beam balance, the beam balance comes to rest at an angle with the horizontal. The beam is supported at a single point P by a pivot. Then which of the following statement (s) is (or are) true?

a) The net torque about P due to the two weights is non-zero at the equilibrium position. b) The whole... View Article

A magnetic wire of dipole moment 4π Am^{2} is bent in the form of a semi-circle. The new magnetic moment is?

a) 1\pi Am^{2} b) 2\pi Am^{2} c) 8i Am^{2} d) 4\pi Am^{2} Solution: c) 8i Am^{2}

Why is electrostatic potential constant throughout the volume of the conductor and has the same value (as inside) on its surface?

Solution:The electric field inside the conductor is zero. \(\begin{array}{l}\Delta V=0\end{array} \) \(\begin{array}{l}V_{1}-V_{2}=0\end{array} \) Or V_{1}=V_{2} means that the potential at... View Article

A proton, a deuteron and an α-particle accelerated through the same potential difference enter a region of uniform magnetic field, moving at right angles to B. What is the ratio of their kinetic energies?

Solutions: Kinetic energy gained by a charged particle of charge q when accelerated under a potential difference V will be... View Article

A man is swinging on a swing made of 2 ropes of equal length L and in direction perpendicular to the plane of paper. The time period of the small oscillations about the mean position is

a) \(\begin{array}{l}2\pi \sqrt{\frac{\sqrt{3}L}{2g}}\end{array} \) b) \(\begin{array}{l}\pi\sqrt{\frac{L}{g}}\end{array} \) c) \(\begin{array}{l}2\pi \sqrt{\frac{L}{2g}}\end{array} \) d) \(\begin{array}{l}2\pi \sqrt{\frac{L}{2\sqrt{3g}}}\end{array} \) The correct answer is a) \(\begin{array}{l}2\pi... View Article

A soldier walks forwards a high wall taking 120steps per minute. When he is at a distance of 90m from the wall he observes that echo of step coincides with the next step. The speed of sound must be?

Solution: In a second, two steps are heard, hence 1 step is heard in 0.5 seconds. Speed= Distance/time Speed =... View Article

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Latest Posts

A parallel beam of light ray parallel to the X-axis is incident on a parabolic reflecting surface x=2by^2 as shown in the figure. After reflecting it passes through focal point F. What is the focal length of the reflecting surface?

A particle executing SHM has a maximum speed of 30cms−1 and a maximum acceleration of 60cms−2 . What is the period of oscillation?

A thin rod of mass m and length 2l is made to rotate about an axis passing through its centre and perpendicular to it. Its angular velocity changes from 0 to ω in time t. What is the torque acting on the rod?

If all linear dimensions of an inductor are tripled, then self inductance will become (keeping total number of turns per unit length constant).

When slightly different weights are placed on the two pans of a beam balance, the beam balance comes to rest at an angle with the horizontal. The beam is supported at a single point P by a pivot. Then which of the following statement (s) is (or are) true?

A magnetic wire of dipole moment 4π Am^{2} is bent in the form of a semi-circle. The new magnetic moment is?

Why is electrostatic potential constant throughout the volume of the conductor and has the same value (as inside) on its surface?

A proton, a deuteron and an α-particle accelerated through the same potential difference enter a region of uniform magnetic field, moving at right angles to B. What is the ratio of their kinetic energies?

A man is swinging on a swing made of 2 ropes of equal length L and in direction perpendicular to the plane of paper. The time period of the small oscillations about the mean position is

A soldier walks forwards a high wall taking 120steps per minute. When he is at a distance of 90m from the wall he observes that echo of step coincides with the next step. The speed of sound must be?

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