Acceleration in 2D

Q.

A body starting from rest travels with uniform acceleration. If it travels $100m$in $5s$, what is the value of acceleration?

Q.

The component of a vector is

1. always less than its magnitude

2. always greater than its magnitude

3. always equal to its magnitude

4. none of these

Q.

If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$, then find the value of $c$.

1. $0.1$

2. $\sqrt{0.11}$

3. $\sqrt{0.8}$

4. $1$

Q.

How will the equations of motion for an object moving with a uniform velocity change?

Q. The coordinates of a particle moving in a plane are given by x(t) = a cos (pt) and y(t) = b sin (pt) where a, b (<a) and p are positive constants of appropriate dimensions. Then

1. the path of the particle is an ellipse
2. the velocity and acceleration of the particle are normal to each other at $t=\pi /\left(2p\right)$
3. the acceleration of the particle is always directed towards a focus
4. the distance travelled by the particle in time interval $t=0tot=\pi /\left(2p\right)$ is a

Q. A uniform force of $(3\hat{i}+\hat{j})N$ acts on a particle of mass 2kg. Hence, the particle is displaced from position $(2\hat{i}+\hat{k})m$ to position $(4\hat{i}+3\hat{j}-\hat{k})m$. The work done by the force on the particle is:

1. 6J
2. 9J
3. 13J
4. 15J

Q.

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are $t_1$ and $t_2$ respectively. Then, the velocity of projection is:

1. $g\sqrt{t_1{t}_2}$

2. $\frac{g\sqrt{t_1{t}_2}}{2}$

3. $\frac{g(t_1+t_2)}{2}$

4. $g\frac{t_1{t}_2}{t_1+t_2}$

Q. A person sitting in an open car moving at constant velocity throws a ball vertically up into air. The ball falls

1. Outside the car
2. In the car ahead of the person
3. In the car to the side of the person
4. Exactly in the hand which threw it up

Q. An electron $(-e,m)$ is given velocity $V_o$ along a uniform electric field $\overrightarrow{E}$. After how much time, electron will return to its original position?

1. $\frac{2m{V}_o}{eE}$
2. $\frac{m{V}_o}{eE}$
3. $\frac{eE}{m{V}_o}$
4. $\frac{2eE}{m{V}_o}$

Q. A particle moves such that its position vector $\overrightarrow{r}\left(t\right)=\cos \omega t\hat{i}+\sin \omega t\hat{j}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\overrightarrow{v}\left(t\right)$ and acceleration $\overrightarrow{a}\left(t\right)$ of the particle:

Q.

Two inclined planes OA and OB having inclination (with horizontal) ${30}^{\circ }$ and ${60}^{\circ }$ respectively , intersect each other at O as shown in figure.A particle is projected from point P with velocity along a direction perpendicular to plane OA. if the particle strickes planne OB perpendicularly at Q, calculate ,

(i) Velocity with which particle strikes the plane OB. (u) 16.25

(ii) Time of flight (v) 20

(iii) Verticla height h of P from O (w) 10

(iv) Maximum height from the ground (x)5

(v) Distance PQ (y)2

1. (i) - (x), (ii) - (u), (iii) - (v), (iv) - (w), (v) - (y)

2. (i) - (w), (ii) - (y), (iii) - (x), (iv) - (u), (v) - (v)

3. (i) - (y), (ii) - (w), (iii) - (x), (iv) - (u), (v) - (v)

4. None of these

Q.

An elevator is descending with uniform acceleration. To measure the acceleration, a person in the elevator drops a coin at the moment the elevator starts. The Coin is 6 ft above the floor of the elevator at the time it is dropped. The person observes that the coin strikes the floor in 1 second. calculate from these data the acceleration of the elevator.

Q.

A body is thrown vertically upward such that the distance travelled by it in fifth and sixth second are equal .the maximum height reached by body is

Q.

A body of mass 2 kg has an initial velocity of 3 m/s along OE and it is subjected to a force of 4

Newton’s in OF direction perpendicular to OE. The distance of the body from O after 4 seconds will be

1. 28 m

2. 20 m

3. 48 m

4. 12 m

Q. Can three vectors, which not in one plane, give a zero resultant?

Q. A ball strikes the floor vertically downward with a speed 5 m/s and rebounds with the same speed the magnitude of change of its velocity will be?

Q.

Assuming that the mass of Earth is $100$ times larger than that of Moon and radius of Earth is about $4$ times as that of Moon, show that the weight of an object on Moon is $\frac{1}{6}\mathrm{th}$ of that on the earth.

Q.

An empty plastic box of mass m is found to acclerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6 ?

Q. In case of projectile motion, what is the acceleration along the horizontal and vertical?

Q. a shell is fired vertically upwards with a velocity v1 from a trolley moving horizontally with velocity v2. a person on the ground observes the motion of the shell as a parabola , whose horizontal range is?

Q. A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $v$ on the distance $x$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)

1. 
2. 
3. 
4. 

Q.

Find the acceleration of the moon with respect to the earth from the following data : Diistance between the earth and the moon = $3.85\times {10}^5$km and the time taken by the moon to complete one revolution around the earth = 27.3 days.

Q. a body thrown vertically upward with initial velocity 52m/s fro ground passes twice a point at h height above at an interval of 10s the height h is

Q.

Find the acceleration due to gravity of the moon at a point 1000 km above the moon's surface. The mass of the moon is $7.4\times {10}^{22}$ kg and its radius is 1740 km.

Q. A body starts from rest and moves with uniform acceleration. Which of the following graphs represent its motion:

1. 
2. 
3. 
4. 

Q.

The distance traveled by a body starting from rest and moving with uniform acceleration is directly proportional to the square of the time.

1. True
2. False

Q.

A healthy youngman standing at a distance of 7 m from 11.8 m high building sees a kid slipping from the top floor. With what speed (assumed uniform) should he run to catch the kid at the arms height (1.8)m ?

Q.

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that centripetal acceleration is varying with time $t$ as $k^{2}r{t}^2$, where $k$ is a constant. The power delivered to the particle by the force acting on it is

1. $m^2{k}^2{r}^2{t}^2$

2. $m{k}^2{r}^{2}t$

3. $m{k}^{2}r{t}^2$

4. $mk{r}^{2}t$

Q.

An NCC parade is going at a uniform speed of 6 km/h through a place under a berry tree on which a bird is siting at a height of 12.1 m. At a particular instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on this uniform.

Q.

The maximum resultant of two forces is$P$and the minimum resultant is$Q$, the two forces are at right angles, the resultant is

1. $P+Q$

2. $P–Q$

3. $\frac{1}{2\left(\sqrt{P^2+Q^2}\right)}$

4. $\sqrt{\frac{P^2+Q^2}{2}}$