OnlineCBT
Physics · MOTION IN A PLANE
Practice questions & answers
Find a question, read its answer and explanation, then practise related questions.
Physics MOTION IN A PLANE · Clear filters
95 questions
Physics · MOTION IN A PLANE
Match List-I with List-II: List-I List-II A Maximum height (\( h_m \)) I \( \frac{v_0^2 \sin 2\theta_0}{g} \) B Time of flight (\( T_f \)) II \( \frac{v_0^2 \sin^2\theta_0}{2g} \) C Horizontal range (\( R \)) III \( \frac{2v_0 \sin\theta_0}{g} \) D Equation of trajectory IV \( x \tan\theta_0 - \frac{g x^2}{2 v_0^2 \cos^2\theta_0} \) Choose the correct answer from the options given below:
Read answer →Physics · MOTION IN A PLANE
For the three-dimensional vector \( \mathbf{A} \) resolved into rectangular components in the figure, if \( A_x = 2\text{ units} \), \( A_y = 3\text{ units} \), and \( A_z = 6\text{ units} \), what is the magnitude of vector \( \mathbf{A} \)?
Read answer →Physics · MOTION IN A PLANE
A particle has an initial velocity \( \vec{v}_0 = (3\hat{i} + 4\hat{j})\text{ m/s} \) and moves with a constant acceleration \( \vec{a} = (0.4\hat{i} + 0.3\hat{j})\text{ m/s}^2 \). Its speed after \( t = 10\text{ s} \) is:
Read answer →Physics · MOTION IN A PLANE
Three coplanar forces \( \mathbf{F}_1 \), \( \mathbf{F}_2 \), and \( \mathbf{F}_3 \) keep a body in static equilibrium. If \( |\mathbf{F}_1| = 5\text{ N} \), \( |\mathbf{F}_2| = 12\text{ N} \), and \( |\mathbf{F}_3| = 13\text{ N} \), what is the angle between the forces \( \mathbf{F}_1 \) and \( \mathbf{F}_2 \)?
Read answer →Physics · MOTION IN A PLANE
A body projected at an angle \( \theta_0 \) to the horizontal follows a parabolic trajectory given by \( y = \sqrt{3}x - \frac{g x^2}{20} \) (where \( x, y \) are in metres and \( g = 10\text{ m/s}^2 \)). The angle of projection \( \theta_0 \) and the initial speed \( v_0 \) are respectively:
Read answer →Physics · MOTION IN A PLANE
A particle moves in a plane from initial position vector \( \mathbf{r}_1 = (2\hat{i} + 3\hat{j})\text{ m} \) to final position vector \( \mathbf{r}_2 = (6\hat{i} + 6\hat{j})\text{ m} \). The magnitude of the displacement vector of the particle is:
Read answer →Physics · MOTION IN A PLANE
A motorboat is racing towards north at \( 25\text{ km/h} \) and the water current in that region is \( 10\text{ km/h} \) in the direction of \( 60^\circ \) east of south. What is the magnitude of the resultant velocity of the boat?
Read answer →Physics · MOTION IN A PLANE
Consider the following statements regarding uniform circular motion: (A) The speed of the particle remains constant. (B) The velocity vector of the particle continuously changes. (C) The centripetal acceleration vector is directed tangentially to the circle. (D) The magnitude of centripetal acceleration is given by \( \omega^2 R \). Which of the above statements are correct?
Read answer →Physics · MOTION IN A PLANE
The rectangular components of a vector in a plane are \( A_x = 6\text{ units} \) and \( A_y = 6\sqrt{3}\text{ units} \). The angle \( \theta \) made by the vector with the positive x-axis is:
Read answer →Physics · MOTION IN A PLANE
A force vector \( \mathbf{F} \) of magnitude \( 20\text{ N} \) makes an angle of \( 30^\circ \) with the horizontal x-axis. Its vertical y-component \( F_y \) is equal to:
Read answer →Physics · MOTION IN A PLANE
Vector \( \mathbf{P} \) has magnitude 6 units and points along the positive x-axis. Vector \( \mathbf{Q} \) has magnitude 10 units and makes an angle of \( 120^\circ \) with the positive x-axis. What is the unit vector along the direction of the resultant vector \( \mathbf{R} = \mathbf{P} + \mathbf{Q} \)?
Read answer →Physics · MOTION IN A PLANE
An insect trapped in a circular groove of radius \( 12\text{ cm} \) moves along the groove steadily and completes \( 7 \) revolutions in \( 100\text{ s} \). What is the angular speed \( \omega \) of the insect? (Take \( \pi = 22/7 \))
Read answer →Physics · MOTION IN A PLANE
Match List-I with List-II: List-I List-II A Magnitude of resultant vector \( R \) I \( \sqrt{A^2+B^2+2AB\cos\theta} \) B Direction angle \( \tan\alpha \) of resultant II \( \frac{B\sin\theta}{A+B\cos\theta} \) C Law of sines for vector triangle III \( \frac{R}{\sin\theta} = \frac{A}{\sin\beta} = \frac{B}{\sin\alpha} \) D Condition for maximum resultant magnitude IV \( \theta = 0^\circ \) Choose the correct answer from the options given below:
Read answer →Physics · MOTION IN A PLANE
A motorboat is heading due north at a speed of \( 25\text{ km/h} \), and the water current in that region is moving at \( 10\text{ km/h} \) in the direction of \( 60^\circ \) east of south. Calculate the magnitude of the resultant velocity of the motorboat relative to the shore.
Read answer →Physics · MOTION IN A PLANE
A vector \( \mathbf{A} = 8\hat{i} + 15\hat{j} \) is expressed as a linear combination \( \mathbf{A} = \lambda \mathbf{a} + \mu \mathbf{b} \), where \( \mathbf{a} = 2\hat{i} \) and \( \mathbf{b} = 3\hat{j} \). The values of real constants \( \lambda \) and \( \mu \) are respectively:
Read answer →Physics · MOTION IN A PLANE
A cricket ball is thrown with a speed of \( 28\text{ m/s} \) at an angle of \( 30^\circ \) above the horizontal. Taking \( g = 9.8\text{ m/s}^2 \), the maximum height achieved by the ball is:
Read answer →Physics · MOTION IN A PLANE
In the given 3D resolution diagram (Fig. 3.9d), a vector \( \mathbf{A} \) makes angles \( \alpha \), \( \beta \), and \( \gamma \) with the x, y, and z axes respectively. If \( \cos\alpha = \frac{1}{2} \) and \( \cos\beta = \frac{1}{\sqrt{2}} \), where \( 0 \le \gamma \le 90^\circ \), determine the value of \( \cos\gamma \), and calculate the z-component \( A_z \) if the magnitude of the vector is \( |\mathbf{A}| = 10\text{ units} \).
Read answer →Physics · MOTION IN A PLANE
A particle starts from the origin at \( t = 0 \) with an initial velocity \( \vec{v}_0 = 5.0\hat{i}\text{ m/s} \) and moves in the xy-plane under a constant acceleration \( \vec{a} = (3.0\hat{i} + 2.0\hat{j})\text{ m/s}^2 \). What is the y-coordinate of the particle at the instant its x-coordinate is \( 84\text{ m} \)?
Read answer →Physics · MOTION IN A PLANE
Two equal vectors \( \mathbf{A} \) and \( \mathbf{B} \), each of magnitude \( 10\text{ units} \), are inclined at an angle of \( 60^\circ \) to each other. Calculate the magnitude of the vector difference \( |\mathbf{A} - \mathbf{B}| \).
Read answer →Physics · MOTION IN A PLANE
In the position and displacement graph shown, if point P has coordinates \( (2, 1)\text{ m} \) and point P' has coordinates \( (6, 4)\text{ m} \), what is the magnitude of the displacement vector \( \mathbf{PP'} \)?
Read answer →Physics · MOTION IN A PLANE
Match List-I with List-II: List-I List-II A Centripetal acceleration (\( a_c \)) I \( \frac{d^2 x}{dt^2}\hat{i} + \frac{d^2 y}{dt^2}\hat{j} \) B Angular speed (\( \omega \)) II \( \omega R \) C Tangential speed (\( v \)) III \( \frac{2\pi}{T} \) D Instantaneous acceleration (\( \mathbf{a} \)) IV \( \frac{v^2}{R} \) Choose the correct answer from the options given below:
Read answer →Physics · MOTION IN A PLANE
