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Find the direction of friction on the block for the figure shown.

The time period of an object performing SHM is $16\text{s}$. It starts its motion from the equilibrium position. After $2\text{s}$ its velocity is $\pi \text{m/s}$. What is its displacement amplitude?

The force exerted by a compression device is given by $F\left(x\right)=kx(x-l)$, where $l$ is the maximum possible compression, $x$ is the compression and $k$ is a constant. The work required to compress the device by a distance $d$ will be maximum when

Find the period of small oscillations of the bob of mass $m$ shown in the figure. Given, mass of the rod is also $m$.

A tank is filled upto height $h$ with a liquid and is placed on a platform of height $h$ from the ground. To get maximum range $x_m$, a small hole is punched at a distance $y$ from the free surface of the liquid. Then find the value of maximum range ($x_m$).

The excess pressure inside the first soap bubble is three times that inside the second bubble. Then, the ratio of the volume of the first bubble to that of the second bubble will be

In the figure shown, find the tension $‘T^{\prime }$ in the string to prevent the body from sliding down the plane. Assume the string to be horizontal.

A particle moves in XY plane such that its position, velocity and acceleration are given by $\overrightarrow{r}=x\hat{i}+y\hat{j};\overrightarrow{v}=v_x\hat{i}+v_y\hat{j};\overrightarrow{a}=a_x\hat{i}+a_y\hat{j}$

which of the following condition is correct if the particles speed is reducing?

A simple harmonic oscillator having four identical springs as shown in figure has time period (neglect the separation between the ends on the roof and the ends connected to the mass):

Derivative of $f\left(x\right)=e^x\sin \left(\sqrt{x}\right)$ is

A sphere of solid material of specific gravity $8$ has a concentric spherical cavity and just sinks in water. The ratio of radius of cavity to that of outer radius of the sphere must be

What is the unit of Density?

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy ($K_t$) as well as rotational kinetic energy ($K_r$) simultaneously. The ratio $K_t:(K_t+K_r)$ for the sphere is

If you performed a work "W" on an object and no external forces are acting on you and the object, while doing this work, which of the following can be true:

A battery consist of a variable number of $n$ identical cells having internal resistance $r$ each. They are connected in parallel. The terminal of battery is short-circuited and the current $I$ is measured. Which of the following graphs give correct relationship between $I$ and $n$?

The capacity of a parallel plate condenser is . When a glass plate is

placed between the plates of the conductor, its potential becomes 1/8thof

the original value. The value of dielectric constant will be

Two projectiles are projected at angles $(\frac{\pi }{4}+\theta )\text{and}(\frac{\pi }{4}-\theta )$ with the horizontal, where $\theta <\frac{\pi }{4}$, with same speed. The ratio of horizontal ranges described by them is

Ten solid spheres of same radius having densities $\rho ,2\rho ,3\rho$... $10\rho$ respectively are put on the $x$ - axis at positions $x=1,x=2,x=3$ ... $x=10$. Find the position of centre of mass of these ten spheres.

A block of mass $1\text{kg}$ slides down on a rough inclined plane of inclination ${60}^{\circ }$ starting from its top. If the coefficient of kinetic friction is 0.5 and the length of the plane is $1\text{m}$, then work done against friction is (Take $g=9.8{\text{m/s}}^2$)

Figure shows a loop-the-loop track of radius R. A car (without engine) starts from a platform at a distance h above the top of the loop and goes around the loop without falling off the track. Find the minimum value of h for a successful looping. Neglect friction.

A uniform solid sphere of radius R, rolling without sliding on a horizontal surface with an angular velocity ${\omega }_0$, meets a rough inclined plane of inclination $\theta ={60}^{\circ }$.The sphere starts pure rolling up the plane with an angular velocity $\omega$ . Find the value of $\omega$.

When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential is 4.8 volts. If the same surface is illuminated with radiation of double the wavelength, then the stopping potential becomes 1.6 volts. Then the threshold wavelength for the surface is

The de-Broglie wavelength associated with the particle of mass m moving with velocity v is

For the resultant of the two vectors to be maximum, what must be the angle between them

Two identical uniform rods $\text{EF}$ and $\text{GH}$, each of length $L=6\text{m}$ are joined as shown in figure. Locate the centre of mass of the frame.

[Point $\text{O}$, which is the point where the axes of the rods meet is the origin]

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as

$x=2cos(0.5\pi t+\frac{\pi }{3})$

The magnitude of the maximum acceleration of the particle in $cm{s}^{-2}$ is

A time varying force is represented as $F=2t\text{N}$. Find out the impulse imparted by this force during the first second.

A ball of mass 0.4 kg moving with uniform speed of $2m{s}^{-1}$ strikes normally a wall and rebounds. Assuming the collision to be elastic and the time of contact of the ball with the wall as 0.4s, find the force exerted on the ball

What will be the modulus of rigidity for water, considering it to be ideal fluid ?

A particle of mass 'm' moving eastward with a speed 'v' collides with another particle of the same mass 'm' and moving northward with the same speed 'v'. The two particles coalesce on collision. The new particle of mass '2'm will move in the north-easterly direction with a velocity

I have an insulator with dielectric constant k. If I place it in a region in vacuum with a field E. Then the net field inside the dielectric will be?

The speed of a freely falling body from rest is proportional to $g^p{h}^q$, where $g$ is acceleration due to gravity and $h$ is the distance travelled. The values of $p$ and $q$ are

An uncharged parallel-plate capacitor having a dielectric of dielectric constant $K$ is connected to a similar air cored parallel-plate capacitor charged to a potential $V_0$. The two share the charge and the common potential becomes $V$. The dielectric constant $K$ is

A street car moves rectilinearly from station A (here car stops) to the next station B (here also car stops ) with an acceleration varying according to the law $f=a-bx$, where $a$ and $b$ are positive constants and $x$ is the distance from station A. The distance between the two stations & the maximum velocity are respectively.

In any Bohr orbit of the hydrogen atom, the ratio of kinetic energy to potential energy of the electron is

A car is moving on a levelled circular road of radius of curvature $300\text{m}$. If the coefficient of static friction is $0.3$ and acceleration due to gravity is $10m{s}^{-2}$, then maximum allowable speed for the car will be (in $km{h}^{-1})$

When two bodies move uniformly towards each other, the distance between them diminishes by $16\text{m}$ every $10\text{s}$. If bodies move in same direction with velocities of the same magnitude as before, the distance between them will decrease by $3\text{m}$ in every $5\text{s}$. The speed of each body is

The energy of a photon is E=hv and the momentum of photon $p=\frac{h}{\lambda }$, then the velocity of photon will be

Two rain drops reach the earth with different terminal velocities having ratio $9:4$. Then the ratio of their volumes is

Refer to the circuit diagram and the corresponding graphs. The current rises when key $K$ is pressed. With $R=R_1$ and $L=L_1$ the rise of current is shown by curve (1), while curve (2) shows the rise of current when $R=R_2$ and $L=L_2$. The maximum current is same for both curves, then :

The equivalent resistance between the points A and B of the circuit shown in figure is.

Given: $v=0.6-0.3t$ (in SI units). The acceleration is

If $y=\frac{\ln x}{x}$, then $\frac{dy}{dx}$ will be

A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $20m{s}^{-1}$. A second player $60m$ away along the direction of kick starts running to receive the ball at that instant. Find the speed with which second player should run to reach the ball before it hits the ground $(g=10m{s}^{-2})$

Match List I with List II and select the correct answer.

$\begin{array}{cc}\text{List I(Physical quantity)}& \text{List II (Dimensions)}\\ \text{A. Force}& {\text{1. T}}^{-1}\\ \text{B. Angular velocity}& {\text{2. MLT}}^{-2}\\ \text{C. Torque}& {\text{3. ML}}^{-1}{\text{T}}^{-2}\\ \text{D. Stress}& {\text{4. ML}}^{-1}{\text{T}}^{-1}\\ & {\text{5. ML}}^2{\text{T}}^{-2}\end{array}$

If velocity of a particle is $v\left(t\right)=(5t-10)\text{m/s}$, the average speed and magnitude of average velocity of the particle in $4\text{sec}$ respectively are