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Two bodies of mass $10\text{ kg}$ and $5\text{ kg}$ moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. Then the ratio between their centripetal acceleration is:
The major product H of the given reaction sequence is: $$ CH_3-CH_2-CO-CH_3 \xrightarrow{HCN} G \xrightarrow{95\% H_2SO_4, \Delta} H $$
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
A ball is projected with a velocity of $10 \text{ m/s}$ at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be:
A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is:
A man sitting in a bus travelling in a direction from west to east with a speed of $40 \text{ km/h}$ observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear:
A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx⁻²ⁿ, where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by:
The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be:
For a smoothly running analog clock, the ratio of the number of rotations made in a day by the hour hand to the second hand, respectively, is:
A particle is executing uniform circular motion with velocity $\vec{v}$ and acceleration $\vec{a}$. Which of the following is true?
A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx⁻²ⁿ where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by:
A ball is thrown vertically downwards with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with the velocity of 80 m/s. The height of the tower is: (assuming g = 10 m/s²)
If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is:
Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of cross-sectional area $A$ of the wire is
A stone falls under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂, and h₃ is:
A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 ms⁻¹ while passing through a distance of 135 m in t seconds. The value of t is:
Dimensional formula of magnetic flux is:
A bus is moving with 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 minimum speed should the scooterist chase the bus?
A stone falls freely under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂ and h₃ is:
Two bodies, A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is: