Question Bank Directory

The angular speed of a flywheel making 120 revolutions/minute is:

The figure shows a body of mass $m$ moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is:

The major product formed in the following conversion is: [Reaction Image Missing - Context suggests Alcohol Dehydration]

Two trains, each $50 \text{ m}$ long, are travelling in the opposite direction with velocities $10 \text{ m/s}$ and $15 \text{ m/s}$. The time of crossing is:

The stress-strain curves are drawn for two different materials $X$ and $Y$. It is observed that the ultimate strength point and the fracture point are close to each other for material $X$ but are far apart for material $Y$. We can say that the materials $X$ and $Y$ are likely to be (respectively):

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2π s. The acceleration of the particle is:

The velocity of a projectile at the initial point A is $(2\hat{i} + 3\hat{j}) \text{ m/s}$. Its velocity (in m/s) at the point B (landing point on the same horizontal plane) is:

An electric fan has blades of length $30\text{ cm}$ as measured from the axis of rotation. If the fan is rotating at $1200\text{ r.p.m}$, the acceleration of a point on the tip of the blade is about:

A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 ms⁻², the velocity with which it hits the ground is:

The speed of a swimmer in still water is $20 \text{ m/s}$. The speed of river water is $10 \text{ m/s}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north is given by:

If the equation for the displacement of a particle moving on a circular path is given by $\theta = 2t^3 + 0.5$ where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particle after 2 sec from its start is:

The height $y$ and the distance $x$ along the vertical plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2)$ meter and $x = 6t$ meter, where $t$ is in second. The velocity with which the projectile is projected is:

The position of a particle is given by $\vec{r}(t) = 4t\hat{i} + 2t^2\hat{j} + 5\hat{k}$, where $t$ is in seconds and $r$ in metres. Find the magnitude and direction of the velocity $v(t)$, at $t=1$ s, with respect to the x-axis.

Two particles $A$ and $B$ are moving in a uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speeds $v_A$ and $v_B$ respectively. Their time periods of rotation are the same. The ratio of the angular speed of $A$ to that of $B$ will be:

A ball is projected from point $A$ with velocity $20 \text{ m s}^{-1}$ at an angle $60^{\circ}$ to the horizontal direction. At the highest point $B$ of the path (as shown in figure), the velocity $v$ (in $\text{m s}^{-1}$) of the ball will be:

For a prism, when the light undergoes minimum deviation, the relationship between the angle of incidence ($i$) and the angle of emergence ($i'$) is:

A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 m/s², the velocity with which it hits the ground will be:

Parsec is a unit of :

Two bodies of mass $10\text{ kg}$ and $5\text{ kg}$ moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. Then the ratio between their centripetal acceleration is:

Which of the following options incorrectly describes the possible range of values for the mole fraction ($x$) of a component in a mixture?