Component of Vectors

Q. A particle undergoes three successive displacements given by $S_1=\sqrt{2}m$ north-east, $S_2=2m$ due south and $S_3=4m$, ${30}^{\circ }$ north of west, then magnitude of net displacement is

1. $\sqrt{14+4\sqrt{3}}m$
2. $\sqrt{14-4\sqrt{3}}m$
3. $\sqrt{4}m$
4. $1-2\sqrt{3}m$

Q. A rigid rod of length $l$ leans against a vertical wall ($y$-axis) as shown in figure. The other end of the rod is on the horizontal floor. Point $\text{A}$ is pushed downwards with constant velocity. Find the path of the COM of the rod is

1. A parabola
2. An ellipse
3. A circle of radius $\frac{l}{2}$ and its center is at origin
4. A circle of radius $\frac{l}{2}$ but its center isn't at origin

Q. A particle is moving along a curve. Then, choose the correct option(s).

1. If its speed is constant, it has no acceleration.
2. If its speed is increasing, the acceleration of the particle is along its direction of motion.
3. If its speed is constant, the magnitude of its acceleration is inversely proportional to its radius of curvature.
4. The direction of its acceleration cannot be along the tangent.

Q. In SHM, when displacement from mean position is maximum,

1. Velocity is minimum in magnitude
2. Acceleration is maximum in magnitude
3. Acceleration is minimum in magnitude
4. Both (A) and (B)

Q. A person moves $20\text{m}$ towards north-east and then moves $20\text{m}$ towards west and then again moves $20\text{m}$ towards north-east and stops. The magnitude of displacement of the person is :

1. $20\sqrt{5-2\sqrt{2}}\text{m}$
2. $20\text{m}$
3. $20\sqrt{5+2\sqrt{2}}\text{m}$
4. None of these

Q. The acceleration of a particle which moves along the positive $\text{x-}$axis varies with its position as shown in the figure. If the velocity of the particle is $0.8\text{m/s}$ at $x=0$, the velocity of the particle at $x=1.4$ is (in $\text{m/s}$)

1. $1.6$
2. $1.2$
3. $1.4$
4. none

Q. A particle is moving on a curve given by $y=2\sin 2x$ ($x$ and $y$ are in metres). The x-component of velocity is always $2m/s$. If the particle starts from origin at $t=0$, then displacement in metres of the particle after $\frac{\pi }{2}s$ is (answer upto 2 decimal places)

Q. A ball of mass m moving with velocity $v_0$ collides a wall as shown in figure. After impact it rebounds with a velocity $\frac{3}{4}{v}_0$. The impulse acting on ball during impact is-

1. $-\frac{3}{4}m{v}_0\hat{i}$
2. $\frac{-5}{4}m{v}_0\hat{i}$
3. $-\frac{m}{2}{v}_0\hat{j}$
4. $None$ $of$ $these$

Q. A particle undergoes three successive displacements given by $S_1=\sqrt{2}m$ north-east, $S_2=2m$ due south and $S_3=4m$, ${30}^{\circ }$ north of west, then magnitude of net displacement is

1. $\sqrt{14+4\sqrt{3}}m$
2. $\sqrt{14-4\sqrt{3}}m$
3. $\sqrt{4}m$
4. $1-2\sqrt{3}m$

Q. A ball moving with velocity of $9m/s$ collides with another similar stationary ball. After the collision both the balls move in directions making an angle of ${30}^o$ with the initial direction. After the collision their speed will be?

1. $2.6m/s$
2. $5.2m/s$
3. $0.52m/s$
4. $52m/s$

Q. A train is moving on a track at 30 m/s. A ball is thrown from it perpendicular to the direction of motion at 30 m/s at ${45}^0$ from horizontal. Find the distance of ball from the point of projection when it strikes the ground.

1. $90\sqrt{3}m$
2. 60 m
3. $30\sqrt{3}m$
4. 90 m

Q. Velocity of the ball A just after the collision is :

1. $(i+\sqrt{3}j)m/s$
2. $(i-\sqrt{3}j)m/s$
3. $(2i+\sqrt{3}j)m/s$
4. $(2i+2j)m/s$

Q. A car travels 6.0 km due North and then 12.0 km ${60}^o$ west of North. Find the magnitude of displacement.

1. 18 km
2. 14 km
3. 16 km
4. 12 km

Q. A particle is moving on a curve given by $y=2\sin 2x$ ($x$ and $y$ are in metres). The x-component of velocity is always $2m/s$. If the particle starts from origin at $t=0$, then displacement in metres of the particle after $\frac{\pi }{2}s$ is (answer upto 2 decimal places)

Q. A particle is moving on a curve given by $y=2\sin 2x$ ($x$ and $y$ are in metres). The x-component of velocity is always $2m/s$. If the particle starts from origin at $t=0$, then displacement in metres of the particle after $\frac{\pi }{2}s$ is (answer upto 2 decimal places)