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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:
A cricket ball is thrown by a player at a speed of $20 \text{ m/s}$ in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is: (Take $g=10 \text{ m/s}^2$)
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 particle moving with uniform speed in a circular path maintains:
Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings (building being $100 \text{ m}$ apart and being of the same height of $200 \text{ m}$) with the same velocity of $25 \text{ m/s}$. When and where will the two bullets collide? ($g=10 \text{ m/s}^2$)
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:
A particle (A) is dropped from a height and another particle (B) is thrown in the horizontal direction with a speed of 5 m/sec from the same height. The correct statement is:
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 starts its motion from rest under the action of a constant force. If the distance covered in the first 10 s is S₁ and that covered in the first 20 s is S₂, then:
The range of a particle when launched at an angle of $15^\circ$ with the horizontal is $1.5\text{ km}$. What is the range of the projectile when launched at an angle of $45^\circ$ to the horizontal?
A particle is executing uniform circular motion with velocity $\vec{v}$ and acceleration $\vec{a}$. Which of the following is true?