Engineering Mechanics Exam Prep
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Engineering Mechanics Exam Prep
English 21 leveled MCQs Free
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10 marks Long answer
A miscreant snatches a purse from a lady and runs away on a motor cycle at an acceleration of 1.5 m/s². A police party standing nearby starts the chase 15 seconds later in the police van driven at 60 m/s. What time would be taken by the police party to catch up the miscreant?
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The time taken by the police party to catch up can be calculated using the equations of motion for both the miscreant and the police van.
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10 marks Long answer
A stone takes 6 seconds to reach the ground after it is dropped from the tower. If the stone is stopped after 2 seconds of its fall and then released again, how much more time it will take to reach the ground? Take g = 10 m/s².
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The stone will take 4 seconds more to reach the ground after being stopped.
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10 marks Long answer
The motion of a particle is defined by the relations: x = t² + 3t and y = t³ - 8t² + 3 where x and y are in meters and t is in seconds. (a) Write the equations defining the motion of the particle in vectorial form (b) calculate the velocity and acceleration of the particle at time t = 2 seconds.
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The vectorial form is \( \mathbf{r}(t) = (t^2 + 3)\hat{i} + (t^3 - 8t^2 + 3)\hat{j} \); velocity and acceleration can be calculated by differentiating the position functions.
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10 marks Long answer
Two cars A and B move at 54 km/hr in the same direction and the car B is 300 m ahead of car A. if the car A is accelerated at 6 m/s² while the car B continues to move with the same velocity, calculate the time taken by car A to overtake car B.
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The time taken can be calculated using kinematic equations considering the initial distance and relative acceleration.
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10 marks Long answer
When a body moves with a velocity V in a circular orbit of radius r, then prove that normal acceleration an = V²/r.
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Normal acceleration is derived from centripetal acceleration formula, \( a_n = rac{V^2}{r} \).
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10 marks Long answer
An automobile enters a curved road at 30 km/hr and then leaves at 48 km/hr. the curved road is in the form of quarter of a circle and has a length of 400 m. if the car travels at a constant acceleration along the curve, calculate the resultant acceleration at both ends of the curve.
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Resultant acceleration can be calculated using both tangential and normal components based on speed change and radius.
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10 marks Long answer
Define work, kinetic energy, and potential energy. Write their mathematical expressions.
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Work is \( W = F \cdot d \); kinetic energy is \( KE = rac{1}{2}mv^2 \); potential energy is \( PE = mgh \).
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4 marks Medium answer
State the work-energy principle and explain its significance in engineering mechanics.
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The work-energy principle states that the work done on an object equals its change in kinetic energy; it helps analyze forces and motion.
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4 marks Medium answer
Define linear impulse and linear momentum. State the impulse-momentum principle.
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Linear impulse is the product of force and time; linear momentum is mass times velocity; the impulse-momentum principle states that impulse equals the change in momentum.
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4 marks Medium answer
Explain the principle of conservation of mechanical energy with a suitable example.
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The principle states that the total mechanical energy remains constant if only conservative forces act; e.g., a pendulum's energy converts between kinetic and potential.
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4 marks Medium answer
Define angular impulse and angular momentum. Write their mathematical expressions.
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Angular impulse is the product of torque and time; angular momentum is the product of moment of inertia and angular velocity.
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4 marks Medium answer
Define rectilinear motion and derive the equations of motion for constant acceleration.
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Rectilinear motion is motion along a straight line; equations of motion are derived from \( v = u + at \), \( s = ut + rac{1}{2}at^2 \), and \( v^2 = u^2 + 2as \).
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4 marks Medium answer
Explain the theory of direct impact between two bodies. Derive the equations for their velocities after impact using conservation of momentum and the coefficient of restitution.
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Direct impact theory involves conservation of momentum and restitution; equations are derived based on initial and final velocities and the coefficient of restitution.
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4 marks Medium answer
Define tangential acceleration and normal acceleration in curvilinear motion.
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Tangential acceleration is the rate of change of speed along the path; normal acceleration is the rate of change of direction.
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2 marks Short answer
Define curvilinear motion.
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Curvilinear motion is motion along a curved path.
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2 marks Short answer
Define uniform motion.
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Uniform motion is motion at a constant speed in a straight line.
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2 marks Short answer
Define work and power.
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Work is the product of force and displacement; power is the rate of doing work.
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2 marks Short answer
Define relative motion.
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Relative motion is the calculation of the motion of an object with respect to another object.
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2 marks Short answer
Draw velocity-time graph.
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A velocity-time graph plots velocity on the y-axis against time on the x-axis.
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2 marks Short answer
Define oblique impact.
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Oblique impact is when two bodies collide at an angle other than 90 degrees.
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2 marks Short answer
Define direct impact.
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Direct impact occurs when two bodies collide head-on.
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