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Two blocks are attached to the pulley as shown in the arrangement.

If the string is inextensible and all surfaces are frictionless, find out the magnitude acceleration of COM of the system. (Take $g=10m/s^2$)

The speed of block $A$ in the system shown in the figure is (String is massless and inextensible)

In the given picture both pulley and string are massless. Pulley is frictionless. Find the acceleration of mass 2m

A constant force $\overrightarrow{F_1}=(2\hat{i}-4\hat{j})\text{N}$ displaces a particle from $(1,-1,2)$ to $(-1,-1,3)$ and then another force $\overrightarrow{F_2}=(3\hat{i}+4\hat{j})\text{N}$ displaces it from $(-1,-1,3)$ to $(5,5,5)$ (displacement being measured in metres). Find the total work done.

A particle is thrown vertically upwards reaches the highest point in 4 seconds . Calculate the Initial speed of throw and maximuum height reached.

A long bar magnet has a pole strength of 10 Am. Find the magnetic field at a point on the axis of the magnet distance of 5 cm from the north pole of the magnet.

If sum of the roots of a quadratic equation is $8$ and their product is $15$, then the quadratic equation is

On mixing $15\text{mL}$ of ethyl alcohol of density $0.70{\text{g mL}}^{-1}$ with $15\text{mL}$ of pure water at $4{}^{\circ }\text{C}$, the resulting solution is found to have a density of $1.02{\text{g mL}}^{-1}$. The percentage contraction in volume is:

Three blocks, each of same mass m, are connected with wires $W_1$ and $W_2$ of same cross- sectional area a and Young's modulus Y. Neglecting friction the strain developed in wire $W_2$ is

A square section of side $20\text{cm}$ is removed from the bigger square of side $40\text{cm}$ as shown in the figure. Find the center of mass of the remaining portion of the square.

Two pulley arrangements of figure given are identical. The mass of the rope is negligible. In fig (a), the mass $m$ is lifted by attaching a mass $2\text{m}$ to the other end of the rope. In fig (b), $m$ is lifted up by pulling the other end of the rope with a constant downward force $F=2mg$. The acceleration of $m$ in the two cases are respectively

Consider the situation in figure. Both the pulleys and the string are light and all the surfaces are frictionless. (a) Find the acceleration of the mass M. (b) Find the tension in the string. (c) Calculate the force exerted by the clamp on the pulley A in the figure.

If the surface shown in the figure is frictionless, and $T_1=6\sqrt{3}N$, find $F$.

An unknown resistance $X$ is connected in a left gap and known resistance $R$ is connected in the right gap of a metre bridge. The balance point is obtained at 60 cm from the left end of the wire. When R is increased by $2\Omega$, the balance point shifts by $10cm$. Find $X$ and $R$ respectively.

A body starts rotating from rest under the influence of a variable torque $\tau =10{\cos }^2\theta$ where, $\tau$ is in $\text{J}$. Find the total work done by the torque to rotate the body from $0^{\circ }$ to ${180}^{\circ }$.

A particle executes linear simple harmonic motion with an amplitude of $3cm$. When the particle is at $2cm$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is

A small cylinder rolling with a velocity v along a horizontal surface encounters a smooth inclined surface. The height 'h' up to which the cylinder will ascend is

Charged +q and -q are placed at -a and +a on x-axis,potential at any point on x-axis is best represented by which graph.

When yellow light is incident on a surface, no electrons are emitted while green light can emit. If red light is incident on the surface, then

A charged particle of mass ‘m’ and charge ‘q’ is accelerated through a potential difference ‘V’. The De Broglie wavelength associated with the particle is

According to Joule's law of heating, heat produced $H=I^{2}Rt,$ where $I$ is current, $R$ is resistance and $t$ is time. If the errors in the measurements of $I$, $R$ and $t$ are 3%, 4% and 6% respectively, then error in the measurement of H is

A stone tied to the end of a string $80\text{cm}$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\text{sec}$, then magnitude of acceleration of the same will be

A body of mass $m$ is launched up a rough inclined plane of angle ${45}^{\circ }$ with the horizontal. If the time of ascent is half the time of descent in covering the same distance, the coefficient of friction is

The sum of the magnitudes of two forces is $18\text{N}$ and the magnitude of their resultant is $12\text{N}$. If the resultant makes an angle of ${90}^{\circ }$ with the smaller force, then find the magnitude of the forces.

A particle travels along the X-axis. Its velocity time graph is shown above.

At what time instant did the particle change its direction of motion?

In the following diagram, pulley $P_1$ is movable and pulley $P_2$ is fixed. The value of angle $\theta$ in case of equilbrium will be

A piece of iron weighs 44.5 gf in the air. If the density of iron is $8.9\times {10}^{3}kg{m}^{-3}$, find the weight of iron piece when immersed in water.

Consider the following statements about the K-4 undersea ballistic missile successfully test fired from INS Arihant:

The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of $x$ from it is $I\left(x\right)$. Which one of the graphs represents the variation of $I\left(x\right)$ with $x$ correctly ?

Which of the following teams did Aston villa beat?

In the set – up shown in the two figures, $T_1$ is the period in the set up in fig. 1 and $T_2$ is the period for the set up in figure 2. Surface of both inclined planes are smooth and the spring constants are as shown. Then $\frac{T_1}{T_2}$ is.

A disc and a ring having same mass M and radius R rotating about its axis which is normal to their plane. If both have the same angular momentum, then the ratio of acceleration of the particles at the circumference of the disc to the ring is

A brass disc and a carbon disc of same radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to that of the carbon disc is
[${\alpha }_B$ and ${\alpha }_C$ are respectively the temperature coefficients of resistance of brass and carbon & ${\rho }_B$ and ${\rho }_C$ are respectively the resistivities of brass and carbon. Neglect linear expansion]

Two simple pendulums of lengths 1 m and 25 m, respectively, are both given small displacement in the same direction at the same instant. If they are in phase after the shorter pendulum has completed n oscillations, then n is equal to

In Bohr theory of hydrogen atom, let r, v and E be the radius of orbit, speed of electron and the total energy of the electron respectively. Which of the following quantities is directly proportional to the quantum number n?

In space wave propagation the relation between height of antenna (h) and range of transmission is (radius of earth = R)

The wavelength of a 1 KeV photon is $1.24\times {10}^{-9}m$. What is the frequency of 1 MeV photon?

Two point masses M are connected to the light rod of length L and it is free to rotate in vertical plane as shown. Calculate the minimum horizontal velocity given to lower mass M so that it completes the circular motion is vertical plane.

A block of mass $2.0\text{kg}$ is pulled up on a smooth incline of angle ${30}^{\circ }$ with the horizontal. If the block moves with an acceleration of $1.0{\text{m/s}}^2$, then the power delivered by the pulling force at a time $4.0\text{s}$ and the average power delivered during the $4.0\text{s}$ after the motion starts are

A boy of mass M is applying a horizontal force to slide a box of mass M' on a rough horizontal surface. The coefficient of friction between the shoes of the boy and the floor is μ and that between the box and the floor is μ'. In which of the following cases it is certainly not possible to slide the box given the boy is not slipping

The surface tension of soap solution is $0.03\text{N/m}$. The work done in blowing to form a soap bubble of surface area $40{\text{cm}}^2$ is:

If $|\overrightarrow{A}|=4$, $|\overrightarrow{B}|=3$ and the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${30}^{\circ }$, then the scalar product of these two vectors is

The angular velocity of a particle is given by $\omega =1.5t-3t^2+2$, the time when its angular acceleration ceases to exist will be -