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A block of mass 2 kg is kept inside a lift. Lift starts moving downward with an acceleration of a = $12m/s^2$. Height of the lift is 4m. Time after which block will strike roof of the lift is (Take g = $10m/s^2$)

1. 7.6

1. 0.85

1. 47

The graph shows the water needed for plants in a certain time.

Find the equation for the above graph.

3 forces are acting on a particle as shown. Find the acceleration of the particle if its mass is 5 kg.

A capacitive transducer is used for measurement of displacement using an opertional amplifier as shown in the figure.





If the capacitance of capacitive transducer is given by $C_x={ϵ}_{0}A/x$. where $A$ is the area of the plates and $x$ is distance between the plate. Then the relationship between the output voltage $V_0$ and input displacement is given by

Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.

Equation of a plane progressive wave is given by $y=A_1\text{sin}\pi (t-\frac{x}{3})$. After reflecting from a rarer medium amplitude of reflected wave becomes $A_2$. The equation of the reflected wave can be

The position vector of four points $A,B,C$ and $D$ are $\hat{i}+\hat{j}+\hat{k},2\hat{i}+5\hat{j},3\hat{i}+2\hat{j}-3\hat{k},\hat{i}-6\hat{j}-\hat{k}$.

Then select the correct relation.

A water tanker filled up to $\frac{2}{3}$rd of its height is moving with a uniform speed. On sudden application of the brake, the water in the tank would

Food is wrapped in aluminum foils. The aluminium is converted into foils due to its:

An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential)energy $E_o$. Its potential energy is

The magnetic flux through a stationary loop, with resistance $R$, varies with time $t$ as $\varphi =at(T-t)$. Here, $a$ is a constant and $T$ is the time period, with appropriate units. The heat generated in the loop during one time period, neglecting the inductance of the loop will be,

A long cylindrical shell carries positive surface charge '$\sigma$' in the upper half and negative surface charge '$-\sigma$' in the lower half. The electric field lines around the cylinder will look like

(figures are schematic and not drawn to scale)

If two discs of moments of inertia $I_1$ and $I_2$, rotating about a collinear axis passing through their centres of mass and perpendicular to their planes with angular speeds ${\omega }_1$ and ${\omega }_2$ respectively in opposite directions are made to rotate combinedly along the same axis, then the magnitude of new angular velocity of the system is

Electrostatic force $F$ on a charge $\frac{Q}{2}$ at an axial point due to a finite line charge varies as $F=\frac{18000}{x^2+4x}$, where $x$ is in metres and is the distance along axial line from one of the ends. The total charge on the line is

In the figure shown, the spring deflects by $\delta$ to position A ( the equilibrium position) when a mass m is kept on it. During free vibration, the mass is at position B at some instant. The change in potential energy of the spring mass system from position A to position B is

Figure shows a string of linear mass density $1.0\text{g/cm}$ on which a wave pulse is travelling.


Find the time taken by the pulse in travelling through a distance of $50\text{cm}$ on the string. Take $g=10{\text{m/s}}^2$

A motorboat travelling at $10m/s$ due North, encounters a current travelling at $5m/s$ due East. Find the magnitude of relative velocity of boat with respect to the current.

A wheel of mass $m=1\text{kg}$ and radius $r=1\text{m}$ is under pure rolling in a straight line as shown in figure.



If $V=2\text{m/s},a=1{\text{m/s}}^2,\alpha =1{\text{rad/s}}^2$ and $\omega =2\text{rad/s}$, find the torque and $K.E$ of the wheel about the contact point.

When is the phase difference, what is the power factor?

Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for t < 0, t > 4 s, 0 < t < 4 s? (b) impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only).

Figure 5.16

A conducting loop of area $5{\text{cm}}^2$ is placed in a magnetic field which varies sinusoidally with time as $B=0.2\sin 300t$. The normal to the coil makes an angle of ${60}^{\circ }$ with the field. The emf induced at $t=\frac{\pi }{900}\text{s}$, is

If an incident light ray parallel to the principal axis is incident at an angle of $i$ as shown in the figure, then find the distance of $Q$ from the centre of curvature $C$ if the angle of incidence is finite (not very small). Here, $R$ is the radius of curvature.

Two parallel rays are travelling in a medium of refractive index ${\mu }_1=\frac{4}{3}$. One of the rays passes through a parallel glass slab of thickness t and refractive index ${\mu }_2=\frac{3}{2}$. The path difference between the two rays due to the glass slab will be

What is the speed of a projectile at a point on its path where it makes an angle of ${45}^{\circ }$ with the horizontal? It is given that the radius of curvature ($R$) of particle at this point is $50\sqrt{2}\text{m}$. Take $g=10{\text{m/s}}^2$.

Angle $\theta$ shown in graph between friction and applied force on a body is :