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A block of mass $m$ suspended from a spring executes vertical SHM of time period $T$ as shown in the figure. The amplitude of the SHM is $A$ and the spring is never in compressed state during the oscillation. The magnitude of minimum force exerted by the spring on the block is

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies ${\omega }_1$ and ${\omega }_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta $p$ with positions $x$ are shown in the figures. If $\frac{a}{b}=n^2$ and $\frac{a}{R}=n$, then the correct equation(s) is(are):

A boy is pushing a ring of mass $2kg$ and radius $0.5m$ with a stick as shown in the figure. The stick applies a normal force of $2N$ on the ring and rolls it without slipping with an acceleration of $0.3m{s}^{-2}$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs, and the coefficient of friction between the stick and the ring is $\left(P/10\right)$ . The value of $P$ is

An aeroplane, with its wings spread $10\text{m}$, is flying at a speed of $180\text{km/h}$ in a horizontal direction. The total intensity of earth's field at that part is $2.5\times {10}^{-4}{\text{Wb/m}}^2$ and the angle of dip is ${60}^{\circ }$. The emf induced between the tips of the plane wings will be :

A woman starts from her home at 9.00 am, walks with a speed of $5km{h}^{-1}$ on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of $25km{h}^{-1}$. Choose suitable scales and plot the x-t graph of her motion.

The vapour pressure of liquid water is 29.8 torr at ${25}^{\circ }\text{C}$. By what factor does the molar volume of water increases as it vaporizes to form an ideal gas under these conditions ? The density of liquid water is $1{\text{g cm}}^{-3}$ at $298\text{K}$.

A vehicle is moving on a road of grade$+4$% at a speed of $20m/s$. Consider the coefficient of rolling friction as $0.46$ and acceleration due to gravity as $10m/s^2$. On applying brakes to reach a speed of $10m/s$, the required braking distance (in m, round off to nearest integer) along the horizontal, is

1. 30

A uniform rod of length $l=3\text{m}$ free to rotate in a vertical plane about a fixed horizontal axis passing through $O$. The rod is allowed to rotate by releasing from it's vertical position. Find the angular velocity of the rod when rod makes an angle $\theta ={60}^{\circ }$ with vertical. (take $g=10{\text{m/s}}^2$)

As shown in figure two identical capacitors are connected to a battery of $V\text{volts}$ in parallel. When capacitors are fully charged, their stored energy is $U_1$. If the key $K$ is opened and material of dielectric constant ${\epsilon }_r=3$ is inserted in each capacitors their stored energy is now $U_2$. Then $\frac{U_1}{U_2}$ will be:

The force – time graph of an impulse acting on a block of mass 0.02 kg is as shown. If the block initially started from rest, what is its velocity once the force ceases to act on it.

For configuration of media of permittivity ${\epsilon }_0,\epsilon ,{\epsilon }_0$ between parallel plates each of area $A$ as shown in the figure; the equivalent capacitance is

• तुमने बरसात पर पहले भी कभी कोई कविता या लोकगीत सुना होगा। उसे नीचे दी गई जगह में लिखो।

• इस कविता को पढ़ते समय तुम्हारे मन में कई चित्र आए होंगे। उनके बारे में बताओ या उनका चित्र बनाओ।

A pendulum clock giving correct time at a place where $g=9.800m{s}^{-2}$ is taken to another place where it loses 24 seconds during 24 hours. Find the value of g at this new place.

Two coils having the same self inductance are arranged in four different configurations as shown in the options. Which of the following configurations has the maximum value of coupling constant?

The length of the two rods made up of the same metal and having the same area of cross-section are 0.6 m and 0.8 m respectively. The temperature between the ends of first rod is ${90}^{\circ }C$ and ${60}^{\circ }C$ and that for the other rod is 150 and ${110}^{\circ }C$ . For which rod the rate of conduction will be greater

Find the equation of the line parallel to the line passing through $(5,7)$ and $(2,3)$ and having $x$ intercept as $-4$

A square loop of side $a$ hangs from an insulating hanger of a spring balance. The magnetic field of strength $B$ present only at its lower edge which carries a current $I$, as shown in the figure. Find the change in the reading of the spring balance if the direction of current is reversed-

A tank contains $100\text{litres}$ of fresh water. A solution containing $1\text{gm/litre}$ of soluble lawn fertilizer runs into the tank at the rate of $1\text{litre/min}$ and the mixture is pumped out of the tank at the rate of $3\text{litres/min}$. Then, the time when the amount of fertilizer in tank is maximum, is
(correct answer + 2, wrong answer - 0.50)

A particle is moving in a circle of radius $R$ in such a way that at any instant the normal and tangential component of its acceleration are equal. If its speed at $t=0$ is $v_0$. The time taken to complete the first two revolutions is

A particle starts from rest, travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment when the particle completes half the circular track is

In the given constraint, what will be the speed of block $R$ $\left(V_R\right)$, if the string is inextensible and pulleys are frictionless?

The diagram of a logic circuit is given below. The output $F$ of the circuit is given by

A circular coil of wire of radius $r$ has $n$ turns and carries a current $i$. The magnetic induction $\left(B\right)$ at a point on the axis of the coil at a distance $\sqrt{3}r$ from its center is-