Browse and search thousands of solved questions for your preparation.
Free questions with full explanations — locked behind signup to protect quality.
The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:
The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20 \text{ m/s}^2$ at a distance of $5 \text{ m}$ from the mean position. The time period of oscillation is:
During simple harmonic motion of a body, the energy at the extreme position is:
A radioactive nucleus ${}_Z^A X$ undergoes spontaneous decay in the sequence ${}_Z^A X \to {}_{Z-1} B \to {}_{Z-3} C \to {}_{Z-2} D$, where $Z$ is the atomic number of element $X$. The possible decay particles in the sequence are
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now be:
The refracting angle of a prism is $A$, and refractive index of the material of the prism is $\cot(A/2)$. The angle of minimum deviation is:
A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^\circ$, the box starts to slip and slides $4.0 \text{ m}$ down the plank in $4.0 \text{ s}$. The coefficients of static and kinetic friction between the box and the plank will be, respectively:
The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^\circ$. One of the two refracting surfaces of the prism is made a mirror inwards with a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:
Two pendulums of length $121 \text{ cm}$ and $100 \text{ cm}$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:
Pick the wrong statement in the context with a rainbow.
A rod of length $10\text{ cm}$ lies along the principal axis of a concave mirror of focal length $10\text{ cm}$ in such a way that its end closer to the pole is $20\text{ cm}$ away from the mirror. The length of the image is:
A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up, to the surface of the liquid and moves along its surface (see figure). How fast is the light traveling in the liquid?
If the critical angle for total internal reflection from a medium to vacuum is $45^{\circ}$, the velocity of light in the medium is:
A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness $3 \text{ cm}$ and a refractive index $1.5$ is placed over the mark. How should the microscope be moved to get the mark in focus again?
A ray of light is incident at an angle of incidence, $i$, on one face of a prism of angle $A$ (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is $\mu$, the angle of incidence $i$, is nearly equal to:
For a normal eye, the cornea of eye provides a converging power of $40\text{ D}$ and the least converging power of the eye lens behind the cornea is $20\text{ D}$. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:
Three blocks with masses $m$, $2m$, and $3m$ are connected by strings as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward at constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)
The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is:
The given electrical network is equivalent to: