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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:
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 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:
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:
A ball is projected with a velocity of $10 \text{ m/s}$ at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be:
A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is:
A man sitting in a bus travelling in a direction from west to east with a speed of $40 \text{ km/h}$ observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear:
A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx⁻²ⁿ, where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by:
The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be:
For a smoothly running analog clock, the ratio of the number of rotations made in a day by the hour hand to the second hand, respectively, is:
A particle is executing uniform circular motion with velocity $\vec{v}$ and acceleration $\vec{a}$. Which of the following is true?
A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx⁻²ⁿ where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by:
A ball is thrown vertically downwards with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with the velocity of 80 m/s. The height of the tower is: (assuming g = 10 m/s²)
If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is:
Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of cross-sectional area $A$ of the wire is
A stone falls under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂, and h₃ is: