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For the given situation, which of the following options correctly represents the equation of the SHM?

Find the acceleration of the two bodies if the system is shown, is at rest initially.
Take $g=10{\text{m/s}}^2$.

The elevator shown in the figure is descending with an acceleration of $2{\text{ms}}^{-2}$. The mass of the block $A=0.5\text{kg}$. The force exerted by the block $A$ on the block $B$ is $(g=10{\text{ms}}^{-2})$

Consider two arrangements of $N$ identical resistors, one in parallel and the other in series. Each of these arrangements are connected to batteries of the same voltage. The ratio of power dissipated in the parallel arrangement to the series arrangement is

A particle of mass $2\text{kg}$ moving with a velocity of $3\text{m/s}$ is acted upon by a force which changes its direction of motion by an angle of ${90}^{\circ }$ without changing its speed. What is the magnitude of impulse experienced by the particle?

Electromagnetic waves emanating from a point A (in air) are incident on a rectangular block of material M and emerge from the other side as shown. The angles I and r are angles of incidence and refraction when the wave travels from air to the medium. Such paths for the rays are possible

If a spring of spring constant $k$ is divided into $m$ equal parts, and all are connected in parallel, then the equivalent spring constant of the combination is

The intensity of light $I_1$ received by the emitter plate in Lenard's photoelectric set-up is changed by moving the source to twice the initial distance. What is the new intensity $I_2$ received by the emitter plate?

A metal plate of mass $200\text{gm}$ is balanced in mid – air by throwing 40 balls /sec, each of mass $2\text{gm}$, vertically upwards from below. The balls rebound with the same speed with which they strike the plate. Find the velocity with which the balls strike the plate. (Take $g=9.8m/s^2$)

A block of mass m can slide freely along the vertical surface of a bigger block of mass M as shown in figure. There is no friction anywhere in the system. The block m is connected to one end of a string whose other end is fixed at point P. The string between $P_1$ and P is horizontal and other parts of the string are vertical. System is released from rest. Find the accelerations of m during their subsequent motion.

A child applies a force $F$ parallel to the $x$-axis to a block moving on a horizontal surface. The $x$-component of the force varies with the $x$-coordinate of the block as shown in figure. The work done by the force $F$ when the block moves from $x=0$ to $x=7\text{m}$ and $x=3\text{m}$ to $4\text{m}$ are (in joules)

A wheel is making rotations about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rot/s in 4 seconds. It's angular acceleration is

A disc of radius $2cm$ rotating uniformly about a stationary axis with an angular velocity of $10rad/s$ is now experiencing an angular retardation of $\alpha =0.2t$. The magnitude of centripetal acceleration at $t=2s$ is

The maximum height of an oblique projectile is $8\text{m}$. The horizontal range is $24\text{m}$. The vertical component of the velocity of projection is

A boat that has a speed of $5kmph$ in still water crosses a river of width $1km$ along the shortest possible path in $15$ minutes. The velocity of the river water in $kmph$ is

A projectile is thrown at an angle of ${60}^{\circ }$ with horizontal. If $E$ is the kinetic energy with which the projectile is thrown, then find the kinetic energy at the top of trajectory.

Three blocks $A,B$ and $C$ of equal masses $‘m^{\prime }$ each are placed one over the other on a frictionless table. The coefficient of friction between any two blocks is $\mu$. Find the maximum value of mass of block $D$ so that the blocks $A,B$ and $C$ move without slipping over each other.

A circular loop of radius $0.3$ cm lies parallel to a much bigger circular loop of radius $20$ cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15$ cm. If a current of $2.0$ A flows through the smaller loop, then the flux linked with bigger loop is :

A boat moves perpendicular to the bank of a stream with a velocity of $7.2\text{km/h}$. The current carries it $150\text{m}$ downstream, the time required to cross the river is
(The width of the river is $0.5\text{km}$)

Two persons pull a rope towards themselves. Each person exerts a force of 100 N on the rope. Find the Young modulus of the material of the rope if it extends in length by 1 cm. Original length of the rope = 2m and the area of cross section = $2c{m}^2.$

F = 4N, m = 2kg, M = 4kg then

Why is intermolecular forces are electromagnetic in nature?

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is $\upsilon$, what is the pressure at another point where the velocity of flow is $2\upsilon ;\rho$ being the density of water?

body of mass 2 kg is moving along positive X direction with a velocity of 5 metre per second now a force of 10 √ 2 newton is applied at an angle of 45 degree with x-axis it's velocity after 3s is

The separation between the plates of a parallel-plate capacitor is 0.500 cm and its plate area is $100c{m}^2.$ A 0.400 cm thick metal plate is inserted into the gap with its faces parallel to the plates. Show that the capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.

The equation of a stationary wave is $y=0.8\text{cos}\left(\frac{\pi x}{20}\right)\text{sin}200\pi t$, where $x$ is in $\text{cm}$ and $t$ is in seconds. The separation between a successive node and antinode will be

The displacement $x$ of a particle along a straight line at time $t$ is given by $x=a_0–a_{1}t+a_2{t}^2$. The acceleration of the particle is:

A body is moving along a rough horizontal surface with an initial velocity $6m/s$. If the body comes to rest after travelling $9m$, then the coefficient of sliding firction will be

A metallic block of mass $20kg$ is dragged with a uniform velocity of $0.5m{s}^{-1}$ on a horizontal table for $2.1s$. The coefficient of static friction between the block and the table is 0.10. What will be the maximum possible rise in temperature of the metal block, if the specific heat of the block is 0.1 C.G.S. unit? Assume $g=10m{s}^{-1}$ and uniform rise in temperature throughout the whole block. [Ignore absorption of heat by the table]

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non - coplanar vectors, then $\frac{a.(b\times c)}{(c\times a).b}+\frac{b.(a\times c)}{c.(a\times b)}=?$

A square loop $ABCD$ having side $l$ carrying a current $i$, is placed at a distance $l/2$; coplanar and parallel with a long straight conductor $XY$ carrying a current $I$, the net force on the loop will be

A block is released from a height $h$ on a track $AB$ as shown in the figure. From $C$ there is a circular track of radius $R=50\text{cm}$.



Assuming all the surfaces to be smooth, the minimum value of $h$ for which the block reaches the point $D$ is

What does infinite resistance mean in circuit.

Ideally we have zero resistance does that mean that if I apply an potential difference V, it will come to zero (because of ohm law)

V=IR

BUT R=0

V=0

What is the percentage increase in length of a wire having diameter $1.5\text{mm}$, stretched by a force of $5\text{kg-wt}$?
(Young's modulus of elasticity of wire $\left(Y\right)=15\times {10}^{11}{\text{dyne/cm}}^2\text{and}g=10{\text{m/s}}^2$)

A balloon going upwards with a velocity of 12m/s is at ht.65 m from earth at any instant.At this instant a packet drops from it.how much time will packet take in reaching earth?

A wooden block is placed on an inclined plane. Angle of inclination is continuously changed. At ${45}^{\circ }$, block starts to slide and continues with uniform speed if angle of inclination is reduced to ${30}^{\circ }$. Find ${\mu }_s$ and ${\mu }_k$

A stone is tied to one end of a string 50 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 10 revolutions in 20 s, what is the magnitude of acceleration of the stone

A straight rod of length L extends form x=a to x=L+a. The gravitational force on a point mass m at x=0 if the mass per unit length of the rod is (A+B$x^2$), is

A particle of mass 10g moves along a circle pf radius 6.4 cm with a constant tangential accelaration. What is the magnitude of this accelaration if the kinetic energy of the particle becomes equal to 8×10^-4 by tye end of the second revolution after the beginning of the motion?

The lowest frequency of light that will cause the emission of photoelectrons from the surface of a metal (for which work function is 1.65 eV) will be

A bullet of mass $50\text{gm}$ is fired from below onto a bob of mass $450\text{gm}$ of a long simple pendulum as shown in the figure. The bullet remains inside the bob and the bob rises through a height of $1.8\text{m}$ vertically upwards. Find the speed of the bullet.

3 particles of masses $2\text{kg}$ each, are placed such that $1^{st}$ one lies on negative $x-$ axis, $2^{nd}$ one lies on negative $y-$ axis and the third one lies on positive $z-$ axis at distances of $2\text{m},3\text{m}$ and $1\text{m}$ respectively from the origin. Then the square of the distance of centre of mass of the system from the origin is