List of practice Questions

Y = A sin($\omega$t+$\phi_0$) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is Y = $\frac{A}{2}$ and it is moving along negative x-direction. Then the initial phase angle $\phi_0$ will be:
A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $\frac{3E}{4}$ then its displacement 'y' is given by :
If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, another mass m is gently fixed upon it. The new amplitude of oscillation will be : 

The function of time representing a simple harmonic motion with a period of \(\frac{\pi}{\omega}\) is:

In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be ________ rad/s when $k = 20 \text{ N/m}$. 

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1/a s. The value of 'a' to the nearest integer is __________.

In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. If each spring has spring constant k, the frequency of oscillation of given body is : 

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :
A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter laying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is _________.
(Take \(g = 10 \text{ m/s}^2\))
Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angles 45\(^\circ\) and 60\(^\circ\) with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is \(\frac{1}{\sqrt{x}}\). The value of x is ________.
A block moving horizontally on a smooth surface with a speed of \( 40 \, ms^{-1} \) splits into two equal parts. If one of the parts moves at \( 60 \, ms^{-1} \) in the same direction, then the fractional change in the kinetic energy will be \( x : 4 \) where \( x = \dots\dots\dots \).
Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be ________ .
The potential energy (U) of a diatomic molecule is $U = \frac{\alpha}{r^{10}} - \frac{\beta}{r^5} - 3$. The equilibrium distance between two atoms will be $\left( \frac{2\alpha}{\beta} \right)^{\frac{a}{b}}$ , where a = _________.
A ball of mass 4 kg, moving with a velocity of 10 ms\(^{-1}\), collides with a spring of length 8 m and force constant 100 Nm\(^{-1}\). The length of the compressed spring is x m. The value of x, to the nearest integer, is __________.

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that $E_{mech} = 8$ J, the incorrect statement for this system is :

[ where K.E. = kinetic energy ] 
 

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:

A small block slides down from the top of hemisphere of radius R=3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is ________ m. (Assume there is no friction between the block and the hemisphere) 

 

A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of $60^\circ$ to the vertical will be ($g = 10 \text{ m/s}^2$) ________ m/s.
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s²) The value of 'x' to the nearest integer is __________. [Note: Usually $h_A = 10$m and $h_B = 5$m in this problem] 

Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B will be A/1, so the value of A will be ______
Two waves are simultaneously passing through a string and their equations are :
\(y_1 = A_1 \sin k(x - vt), y_2 = A_2 \sin k(x-vt+x_0)\). Given amplitudes \(A_1 = 12\) mm and \(A_2 = 5\) mm, \(x_0=3.5\) cm and wave number \(k=6.28\) cm\(^{-1}\). The amplitude of resulting wave will be __________ mm.
Two travelling waves produces a standing wave represented by equation. \(y = 1.0 \text{ mm} \cos(1.57 \text{ cm}^{-1})x \sin(78.5 \text{ s}^{-1})t\). The node closest to the origin in the region \(x>0\) will be at \(x = \)_________ cm.
Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is _________ Hz.