A particle moves in the x-y plane according to rule x = asinωt and y = acosωt . The particle follows:

a straight line path inclined equally to the x and y-axis.

A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of 1 m will the be

In the ratio of the difference in the square roots of the integers i.e. 1 , 2 - 1 , 3 - 2 , 4 - 3

All equal, being equal to 2 / g second

In the ratio of the square roots of integers 1,2,3....

In the ratio of the reciprocal of the square roots of the integers, i.e., 1 1 , 1 2 , 1 3 , 1 4

A particle moves so that its position vector is given by r → = cosωt x ^ + sinωt y ^ , where ω is a constant. Which of the following is true?

Velocity is perpendicular to r → and acceleration is directed towards to origin.

Velocity and acceleration both are parallel to r → .

Velocity is parallel to r → and acceleration is directed away from the origin.

Velocity and acceleration both are perpendicular to r → .

Two particles A and B, move with constant velocities v 1 and v 2 respectively. At the initial moment, their position vectors are r 1 and r 2 respectively. The condition for particles A and B for their collision will be

r 1 - r 2 r 1 - r 2 = v 2 - v 1 v 2 - v 1

The position vector of a particle R as a function of time t is given by R → = 4 sin 2 πt i ^ + 4 cos 2 πt j ^ Where R is in meters, t is in seconds and i ^ , j ^ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

Magnitude of the velocity of the particle 8 m/s.

Acceleration is along - R → .

Magnitude of the acceleration vector is v 2 R , where v is the velocity of the particle.

Path of the particle is a circle of radius 4m.

Physics - Motion Plane - Quiz-5

Two particles A and B, move with constant velocities v₁ and v₂respectively. At the initial moment, their position vectors are r₁ and r₂ respectively. The condition for particles A and B for their collision will be

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$\frac{r_{1} - r_{2}}{|r_{1} - r_{2}|} = \frac{v_{2} - v_{1}}{|v_{2} - v_{1}|}$
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$r_{1} \cdot v_{1} = r_{2} \cdot v_{2}$
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$r_{1} \times v_{1} = r_{2} \times v_{2}$
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$r_{1} - r_{2} = v_{1} - v_{2}$

The position vector of a particle R as a function of time t is given by
$\vec{R} = 4 \sin [2 πt] \hat{i} + 4 \cos [2 πt] \hat{j}$
Where R is in meters, t is in seconds and $\hat{i}, \hat{j}$ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

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Acceleration is along $- \vec{R}$ .
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Magnitude of the acceleration vector is $\frac{v^{2}}{R}$ , where v is the velocity of the particle.
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Magnitude of the velocity of the particle 8 m/s.
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Path of the particle is a circle of radius 4m.

A bus moves over a straight level road with a constant acceleration a. A body in the bus drops a ball outside. The acceleration of the ball with respect to the bus and the earth are respectively

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a and g
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a + g and g - a
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$\sqrt{a^{2} + g^{2}} a n d g$
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$\sqrt{a^{2} + g^{2}} a n d a$

The velocity of a projectile at the initial point A is $(2 \hat{i} + 3 \hat{j})$ m/s. Its velocity (in m/s) at point B is:

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$2 \hat{i} - 3 \hat{j}$
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$2 \hat{i} + 3 \hat{j}$
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$- 2 \hat{i} + 3 \hat{j}$
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$- 2 \hat{i} - 3 \hat{j}$

A particle moves in a circle of radius 5 cm with constant speed and time period $0.2 π$ sec. The acceleration of the particle is:

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25 m/s²
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36 m/s²
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5 m/s²
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15 m/s²

A missile is fired for a maximum range with an initial velocity of 20 m/s. If g= 10 m/s², then the range of the missile will be

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50 m
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60 m
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20 m
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40 m

A particle has initial velocity $(3 \hat{i} + 4 \hat{j})$ and has acceleration $(0.4 \hat{i} + 0.3 \hat{j})$ . Its speed after 10 s is

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7 units
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7 $\sqrt{2}$ units
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8.5 units
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10 units

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground, the magnitude of change in its momentum will be:

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$2 mv$
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$mv / \sqrt{2}$
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$mv \sqrt{2}$
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zero

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are ( $\sqrt{3}$ , 3). The path of the particle makes with the x-axis an angle of:

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30^o
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45^o
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60^o
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0^o

For a projectile projected at angles (45°-θ) and (45°+θ), the horizontal ranges described by the projectile are in the ratio of:

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1:1
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2:3
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1:2
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2:1

A car turns at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap, respectively, is :

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0,0
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0, 10 m/s
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10 m/s, 10 m/s
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10 m/s, 0

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 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 stroke w.r.t north is given by:

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45 $°$ west of north
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30 $°$ west of north
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0 $°$ west of north
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60 $°$ west of north

Two particles A and B are moving in a uniform circular motion in concentric circles of radii $r_{A} a n d r_{B}$ with speeds $v_{A} a n d v_{B}$ respectively. Their time periods of rotation are the same. The ratio of angular speed of A to that of B will be:

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1: 1
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$r_{A} : r_{B}$
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$v_{A} : v_{B}$
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$r_{B} : r_{A}$

A particle starts from rest at t=0 and undergoes an acceleration a in ms^-2 with time t in second which is as shown

Which one of the following plot represents velocity v in ms^-1 versus time t in second?

0:0:1

Practice Physics Quiz Questions and Answers

0:0:1

Practice Physics Quiz Questions and Answers

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