A certain simple harmonic vibrator of mass 0.1 kg has a total energy of 10 J. Its displacement from the mean position is 1 cm when it has equal kinetic and potential energies. The amplitude A and frequency n of vibration of the vibrator are
A large cylindrical container has a base diameter of 3 m. It is filled with a non-viscous liquid up to a height of 2 m. The minimum horizontal acceleration of the container so that the pressure at the point A of the container becomes equal to the atmospheric pressure is
The frequency of a sonometer wire is f, but when the weights producing the tensions are completely immersed in water the frequency becomes f/2 and on immersing the weights in a liquid the frequency becomes f/3. The specific gravity of the liquid is
Blocks shown in figure have equal masses m each. The system is released from rest with the spring unstretched. The string between A and ground is cut when there is maximum extension in the spring. The acceleration of centre of mass of the system of two blocks immediately after the string is cut is
A particle of mass m (starting from rest) moves vertically upwards from the surface of earth under an external force \[\overrightarrow{F}\] which varies with height z as,\[\overrightarrow{F}=\left( 2-\alpha z \right)m\overrightarrow{g}\], where \[\alpha \] is a positive constant. If H is the maximum height to which particle rises, then which of the following is/are correct?
A)
\[H=\frac{2}{\alpha }\]
doneclear
B)
Work done by \[\overrightarrow{F}\]during motion up to \[\frac{H}{2}\]is \[\frac{3mg}{2\alpha }\]
doneclear
C)
Velocity of particle at \[\frac{H}{2}\]is\[\sqrt{\frac{g}{\alpha }}\]
Vectors \[\overrightarrow{a}\] and \[\overrightarrow{b}\] include an angle \[\theta \] between them. If \[\left( \overrightarrow{a}+\overrightarrow{b} \right)\] and \[\left( \overrightarrow{a}-\overrightarrow{b} \right)\] respectively subtend angles \[\alpha \] and \[\beta \] with \[\overrightarrow{a}\] then \[\left( \tan \alpha +\tan \beta \right)\]is )
A disc of radius R=10 cm oscillates as a physical pendulum about an axis perpendicular to the plane of the disc at a distance r from its centre. If \[r=\frac{R}{4}\], the approximate period of oscillation is \[\left( Take\,\,\,\,g=10\,\,\,\,m{{s}^{-2}} \right)\]
A uniform solid disc of radius R and mass m is free to rotate on a frictionless pivot through a point on its rim. The disc is released from rest in the position where the diameter through the pivot is along horizontal. The speed of its centre of mass when the diameter through the pivot is vertical is
Sound of frequency \[1000\text{ }Hz\] from a stationary source is reflected from an object approaching the source at\[30\text{ }m{{s}^{-1}}\], back to a stationary observer located at the source. The speed of sound in air is \[330m{{s}^{-1}}\]. The frequency of the sound heard by the observer is
Four identical mirrors are made to stand vertically to form a square arrangement as shown in a top view. A ray starts from the midpoint M of mirror AD and after two reflections reaches corner D. Then, angle \[\theta \] must be
Statement-1: A sphere is performing pure rolling on a rough horizontal surface with constant angular velocity, frictional force acting on the sphere is zero.
Statement-2: Velocity of contact point is zero.
A)
Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
doneclear
B)
Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
Statement-1: A common model of a solid assumes the atoms to be points executing SHM about mean lattice positions. This model cannot explain thermal expansion of solids.
Statement-2: The average distance over a time period of oscillation between the particles remains constant.
A)
Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
doneclear
B)
Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
