Physics Exam Preparation
Full explanation, worked examples & memory tricks in the app
Physics Exam Preparation
English 23 leveled MCQs Free
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Sample questions with model answers
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5 marks Long answer
A particle moves along the X-axis from $x = 0$ to $x = 5$ m under the influence of a force given by $F = 7 - 2x + 3x^2$. Find the work done in the process.
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Work done is calculated using $W = \int F \, dx$.
The full exam-length answer is in the app.
5 marks Long answer
Prove that the time of flight T and the horizontal range R of a projectile are connected by the equation $gT^2 = 2R \tan \theta$ where \( \theta \) is the angle of projection.
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Use kinematic equations to derive the relation.
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5 marks Long answer
(a) What is escape velocity? Derive its expression and give its value for Earth.
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Escape velocity is $v_e = \sqrt{\frac{2GM}{R}}$; for Earth, $v_e \approx 11.2 \, km/s$.
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5 marks Long answer
A body starting from rest accelerates uniformly along a straight line at the rate of $10 m/s^2$ for 5 s. It then moves for 2 s with uniform velocity of 50 m/s. Then it retards uniformly and comes to rest in 3 s. Draw velocity-time graph of the body and find the total distance traveled by the body.
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Total distance is calculated from the area under the velocity-time graph.
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5 marks Long answer
(a) Show trajectory of a projectile fired with a velocity u making an angle $\theta$ with the vertical is parabolic. Hence derive expressions for maximum height and time of flight.
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Trajectory is parabolic; $H = \frac{u^2 \sin^2 \theta}{2g}, T = \frac{2u \sin \theta}{g}$.
The full exam-length answer is in the app.
5 marks Long answer
(a) Differentiate between angular acceleration and centripetal acceleration. Hence derive an expression for the centripetal acceleration of a particle moving with uniform speed v along a circular path of radius r.
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Centripetal acceleration is $a_c = \frac{v^2}{r}$.
The full exam-length answer is in the app.
5 marks Long answer
(a) What do you mean by banking of a curved road? Derive an expression for velocity of a car on a banked circular road having coefficient of friction $\mu$ and $v > v_0$. Write the expression for optimum velocity of the car.
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Banking helps in reducing reliance on friction; $v = \sqrt{rg(\tan \theta + \mu)/(1 - \mu \tan \theta)}$.
The full exam-length answer is in the app.
5 marks Long answer
(a) What is Impulse-momentum theorem? Figure below shows the position-time graph of a particle of mass 4 kg. What is the (i) force acting on the particle for $t < 0$, $t > 4$ s, $0 < t < 4$ s? (ii) impulse at $t = 0$ and $t = 4$ s? Assume that the motion is one dimensional.
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Impulse-momentum theorem states $J = \Delta p$; calculate force from slope of position-time graph.
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3 marks Medium answer
(b) A smooth block is released at rest on a 45° incline and then slides a distance d. If the time taken to slide on rough incline is n times as large as that to slide than on a smooth incline, find the co-efficient of friction in terms of n.
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Use $\mu = \frac{g}{n g \sin 45°}$.
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3 marks Medium answer
Two uniform solid spheres of equal radii R, but mass M and 4M have a centre to centre separation 6R. Show minimum speed of the projectile so that it reaches the surface of the second sphere is given by $v = \sqrt{\frac{3G M}{5 R}}$.
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Use gravitational potential energy and kinetic energy principles.
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3 marks Medium answer
A body of mass m is suspended by two strings making angles $\alpha$ and $\beta$ with the horizontal. Calculate the tensions in the two strings.
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Use equilibrium conditions to find $T_1$ and $T_2$.
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3 marks Medium answer
By using dimensional analysis, derive an expression for the height (h) to which a liquid of density ($\rho$) and surface tension (S) will rise in a capillary tube of radius (r). Given acceleration due to gravity is g and $h \propto 1/r$.
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Use dimensional analysis to find $h = \frac{2S}{\rho g r}$.
The full exam-length answer is in the app.
3 marks Medium answer
(a) Two springs A and B with constants $K_A$ and $K_B$ ($K_A > K_B$) are given. In which of the springs more work is to be done if, (i) they are stretched by the same amount; (ii) they are stretched by same force.
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More work is done in spring A when stretched by the same amount.
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3 marks Medium answer
(b) The height y and the distance x along the horizontal plane of a projectile on a certain plane (with no atmosphere) are given by $x = (6t)$ metre; $y = (8t - 5t^2)$ metre where t is in seconds. What is the velocity with which the projectile is projected?
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Velocity is calculated from $v = \sqrt{(6^2 + (8 - 10t)^2)}$.
The full exam-length answer is in the app.
3 marks Medium answer
(b) A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?
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Centripetal acceleration is calculated as $a_c = \frac{v^2}{r}$.
The full exam-length answer is in the app.
3 marks Medium answer
(b) A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is $10^6$ kg. What is the angle of banking required to prevent wearing out of the rail?
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Calculate angle using $\tan \theta = \frac{v^2}{rg}$.
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1 marks Short answer
(a) Define angle of repose and angle of friction.
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Angle of repose is the steepest angle of a slope at which a material remains at rest.
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1 marks Short answer
(b) An elephant and an ant are to be projected out of earth into space. Do we need different velocities to do so? Justify.
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No, both need the same escape velocity regardless of mass.
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1 marks Short answer
(b) A spring is cut into two equal halves. How is spring constant of each half affected?
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Each half has a spring constant $2K$.
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1 marks Short answer
(i) A body weighs 63 N on the surface of the earth. How much will it weigh at a height equal to half the radius of the earth?
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28 N
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1 marks Short answer
(ii) Assuming the earth to be a sphere of uniform mass density, what is the weight of a body when it is taken to the end of tunnel 32 km below the surface?
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1/20 times
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1 marks Short answer
(iii) If $g_p$ is the acceleration due to gravity at the poles and $g_e$ that at the equator, then which one is greater?
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$g_p$
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1 marks Short answer
(iv) If a tunnel is dug along a diameter of the earth and body is dropped from one end of the tunnel then how will the body move in the tunnel?
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it will execute SHM about the centre.
The full exam-length answer is in the app.
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