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A car turns at a constant speed on a circular track of radius $100 \text{ m}$, taking $62.8 \text{ s}$ for every circular lap. The average velocity and average speed for each circular lap, respectively, is:
A string is stretched between fixed points separated by $75.0 \text{ cm}$. It is observed to have resonant frequencies of $420 \text{ Hz}$ and $315 \text{ Hz}$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:
A source of sound S emitting waves of frequency $100 \text{ Hz}$ and an observer O are located at some distance from each other. The source is moving with a speed of $19.4 \text{ m/s}$ at an angle of $60^{\circ}$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330 \text{ m/s}$), is:
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metre long. The length of the open pipe will be
A source of sound S emitting waves of frequency $100 \text{ Hz}$ and an observer O are located at some distance from each other. The source is moving with a speed of $19.4 \text{ ms}^{-1}$ at an angle of $60^\circ$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330 \text{ ms}^{-1}$), is:
The engine of a motorcycle can produce a maximum acceleration of $5 \text{ m/s}^2$. Its brakes can produce a maximum retardation of $10 \text{ m/s}^2$. What is the minimum time in which it can cover a distance of $1.5 \text{ km}$?
A man throws balls with the same speed vertically upwards one after the other at an interval of $2 \text{ seconds}$. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given $g=9.8 \text{ m/s}^2$)
An aeroplane is flying horizontally with a velocity $u = 600\text{ km/h}$ at a height of $1960\text{ m}$. When it is vertically at a point $A$ on the ground, a bomb is released from it. The bomb strikes the ground at point $B$. The distance $AB$ is:
A particle shows a distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:
A car starts from rest and accelerates at $5 \text{ m/s}^2$. At $t=4 \text{ s}$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6 \text{ s}$? (Take $g=10 \text{ m/s}^2$)
A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R$. The angle of projection, $\theta$ is then given by:
The graph that shows the correct variation of $\frac{1}{v}$ with $\frac{1}{u}$ for a concave mirror, where $u$ is the object distance and $v$ is the image distance, is:
A particle moves a distance x in time t according to equation x = (t + 5)⁻¹. The acceleration of the particle is proportional to:
The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms⁻², in the third second is
A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is
A lift is going up. The total mass of the lift and the passenger is 1500 kg. The variation in the speed of the lift is as given in the graph. The height to which the lift takes the passenger is
A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 s another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v? (take g = 10 ms⁻²)
A bus is moving at a speed of 10 ms⁻¹ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?
A particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:
A person travelling in a straight line moves with a constant velocity v₁ for a certain distance x and with a constant velocity v₂ for the next equal distance. The average velocity v is given by the relation: