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A gravitational field is present in a region, and a mass is shifted from $A$ to $B$ through different paths as shown. If $W_1$, $W_2$ and $W_3$ represent the work done by the gravitational force along their respective paths, then:
The spring extends by $x$ on loading, then energy stored by the spring is: (if $T$ is the tension in the spring and $k$ is the spring constant)
The potential energy of a system increases if work is done:
An engine pumps water through a hosepipe. Water passes through the pipe and leaves it with a velocity of $2\text{ m/s}$. The mass per unit length of water in the pipe is $100\text{ kg m}^{-1}$. What is the power of the engine?
Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is:
Two sources of sound placed close to each other, are emitting progressive waves given by $y_1 = 4 \sin(600\pi t)$ and $y_2 = 5 \sin(608\pi t)$. An observer located near these two sources of sound will hear
A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27^\circ\text{C}$, two successive resonances are produced at $20 \text{ cm}$ and $73 \text{ cm}$ column length. If the frequency of the tuning fork is $320 \text{ Hz}$, the velocity of sound in air at $27^\circ\text{C}$ is:
A stone of mass $1 \text{ kg}$ tied to a light inextensible string of length $L = \frac{10}{3} \text{ m}$ is whirling in a circular path of radius $L$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if $g$ is taken to be $10 \text{ m/s}^2$, the speed of the stone at the highest point of the circle is:
A mass of $0.5 \text{ kg}$ moving with a speed of $1.5 \text{ m/s}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50 \text{ N/m}$. The maximum compression of the spring would be:
A force $F = (20 + 10y)$ acts on a particle in the $y$-direction where $F$ is in Newton and $y$ is in metre. The work done by this force to move the particle from $y = 0$ to $y = 1$ m is:
A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\frac{\lambda_2}{\lambda_1}$ is:
A ball moving with velocity $2\text{ m s}^{-1}$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $\text{m s}^{-1}$) after collision will be:
The potential energy of a long spring when stretched by 2 cm is $U$. If the spring is stretched by 8 cm, the potential energy stored in it is:
A body of mass 1 kg is thrown upwards with a velocity 20 ms$^{-1}$. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (Take g = 10 ms$^{-2}$)
The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8 \text{ s}$ is:
Two identical balls A and B having velocities of $0.5 \text{ m/s}$ and $-0.3 \text{ m/s}$ respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be:
An organ pipe filled with a gas at $27^\circ\text{C}$ resonates at $400\text{ Hz}$ in its fundamental mode. If it is filled with the same gas at $90^\circ\text{C}$, the resonance frequency at the same mode will be:
An electric lift with a maximum load of $2000\text{ kg}$ (lift + passengers) is moving up with a constant speed of $1.5\text{ ms}^{-1}$. The frictional force opposing the motion is $3000\text{ N}$. The minimum power delivered by the motor to the lift in watts is : $(g = 10\text{ ms}^{-2})$
The ratio of radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is
A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : ($g = 10 \text{ m/s}^2$)