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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 point $B$ (the point where it hits the ground at the same horizontal level) is:
The viscous drag acting on a metal sphere of diameter $1 \text{ mm}$, falling through a fluid of viscosity $0.8 \text{ Pa-s}$ with a velocity of $2 \text{ m s}^{-1}$ is nearly equal to:
A particle is moving in a horizontal circle with constant speed. It has constant:
A boat crosses a river with a velocity of $8 \text{ km/h}$. If the resulting velocity of boat is $10 \text{ km/h}$, then the velocity of river water is:
A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 s his displacement relative to the ground will be:
A particle moves so that its position vector is given by $\mathbf{r} = \cos(\omega t)\hat{x} + \sin(\omega t)\hat{y}$ where $\omega$ is a constant. Based on the information given, which of the following is true?
A particle has an initial velocity $(3\hat{i} + 4\hat{j})$ and an acceleration $(0.4\hat{i} + 0.3\hat{j})$. Its speed after $10 \text{ s}$ is:
Two non-mixing liquids of densities $\rho$ and $n\rho$ ($n>1$) are put in a container. The height of each liquid is $h$. A solid cylinder floats with its axis vertical and length $L$. The length of the cylinder inside the denser liquid is $pL$ ($p<1$). The density of the cylinder is $d$. The density $d$ is equal to:
The $x$ and $y$ coordinates of the particle at any time are $x = 5t - 2t^2$ and $y = 10t$ respectively, where $x$ and $y$ are in metres and $t$ is in seconds. The acceleration of the particle at $t = 2$ s is:
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:
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: