Review Test 01

A parallel plate capacitor has a capacitance of $C_0$ and an energy storage of $W_0$ with air as the medium. If the air is replaced by glass with a dielectric constant of 5, the new capacitance and energy stored will be?

A $5 \mu F$ capacitor is connected in series with a $10\mu F$ capacitor. If a 300V potential difference is applied across the combination, the energy stored in the capacitors will be?

A parallel plate capacitor has a capacitance $C$. Two parallel conducting plates with the same material and area are placed between the plates of the original capacitor. Each new plate has a thickness equal to $\frac{1}{5}$ of the distance between the original capacitor plates. What is the new capacity of this system?

A body starts from rest and has an acceleration $a$ (in $m/s^2$) that varies with time $t$ (in seconds) according to the equation $a = 3t + 4$. What is the velocity of the body at $t = 2$ seconds?

A projectile fired at an angle of 15° has a horizontal range of 50 m. If the same projectile is fired with the same speed at an angle of 45°, what is the range?

Rain is falling vertically downward at 3 km/h. A man walks in the rain at 4 km/h. With what velocity do the raindrops fall with respect to the man?

A car is traveling at 20 m/s on a straight road. The driver applies the brakes, producing a constant deceleration of $2 \frac{m}{s^2}$. What is the distance traveled by the car in the 3rd second after the brakes are applied?

If I stand at rest on a horizontal floor, it pushes upwards on my feet with a force equal to my weight Mg, where M is my mass. Which of the following is Newton's third-law pair to this upward force on my feet?

A dipole is placed parallel to a uniform electric field. If W is the work done in rotating the dipole by 60°, then what is the work done in rotating the dipole by 180°?

A train moving north at 10 m/s has a length of 150 m. A parrot flies parallel to the train towards the south at 5 m/s. What is the time taken by the parrot to cross the train?

If $\sqrt{3}y = 3x - 1$, then what is the slope of the line?

Find the minimum value of the function $y = 2x^2 - 2x + 3$

What is the area of a rectangular field (in $m^2$) after rounding off the value with correct significant digits, with a length of 55.6m and a breadth of 25m?

In the given circuit, what is the potential difference between points A and B?

If the sum of two unit vectors is a unit vector, then what is the magnitude of their difference?

If $\vec{a} = \hat{i} + \hat{j}$ and $\vec{b} = \hat{j} + \hat{k}$, what is the area of the parallelogram formed by $\vec{a}$ and $\vec{b}$?

Given that $0.2\hat{i} + 0.6\hat{j} + a\hat{k}$ is a unit vector. What is the value of $a$?

Two balls are dropped from the same height at a 1-second time interval. What is the separation between the two balls after 3 seconds from the drop of the 1st ball?

A block of mass $M$ slides down on a rough inclined plane with constant velocity. If the angle made by the inclined plane with the horizontal is $\theta$, what is the magnitude of the contact force?

Assertion (A): An electric fan continues to rotate for some time after the current is switched off. Reason (R): Fan continues to rotate due to inertia of motion. Based on the statements, which of the following is the most appropriate answer?

At a place where the acceleration due to gravity is $10 \frac{m}{s^2}$, a force of 5 kg-wt acts on a body of mass 10 kg, initially at rest, in a horizontal direction. What is the velocity of the body after 4 s?

What will be the reading on the spring balance in the diagram?

Two spheres of equal radii having charges 10C and 6C are placed at some separation. If both spheres are connected by a wire then the ratio of initial to final force between them is:

Inside a hollow charged spherical conductor, the potential is:

If an electron has an initial velocity in an oblique direction from that of a uniform electric field, the path of the electron is:

The electric potential V at any point x, y, z (all in metres) in space is given by $V = 3x^3$ volt. What is the electric field at the point (1m, 0, 2m) in volt/metre ?

The insulation property of air breaks down at $E = 3 \times 10^6 \frac{volt}{meter}$. The maximum charge that can be given to a sphere of diameter 5 m is approximately equal to what coulombs ?

How much kinetic energy will be gained by an $\alpha$ particle in going from a point at 70 V to another point at 50 V?

In the given circuit, what is the reading of the ammeter?

Find the equivalent resistance between points A and B:

An electric cell of e.m.f. E is connected across a copper wire of diameter d and length l. The drift velocity of electron in the wire is $V_d$. If the length of the wire is increased to 2l, what will the new drift velocity of electron be?

If the current through 8$\Omega$ is 2A, then find the potential difference across A and B.

A cell has an emf of 5V. When connected across an external resistance of $2\Omega$ the terminal potential difference falls to 2V. What is the internal resistance of the cell?

In a meter bridge experiment a resistance A on left end is balanced against resistance B at a point which is 40 cm from left end of wire. If resistance A is doubled then find new balancing point from same end.

Three capacitors are connected as shown in the figure. What will the charge on $C_1$ be?

Consider 3 concentric spherical shells of radii R, 2R, and 3R having charges Q, $\frac{Q}{3}$, and -2Q respectively. The Intermediate shell is now grounded, then what is the charge flow into the earth?

A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has a total 25 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?

If the vibration frequency f of the star is given by the following equation: $f = KR^a \rho^b G^c$ where R is the radius of the star, $\rho$ is the density of star, G is the universal gravitational constant and K is a dimensionless constant, then what is the value of (b + c)?

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. The screw gauge has a zero error of -0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is:

Trajectory of a particle in projectile motion is given by: $y=x-\frac{x^2}{80}$. Based on the information, what will be the Horizontal range?

Two bodies of mass $m_1$ and $m_2$ are connected by a string which passes over frictionless massless pulley .If pulley is moving then tension in String is

An object is thrown from a point A horizontally from a tower and hits the ground 3 sec later at point B. The line from A to B makes an angle $30^\circ$ with the horizontal. What is the initial velocity of the object?

If the block shown in the figure does not move, what is the maximum value of force F?

A block is kept on a frictionless inclined surface with angle of inclination $\theta$. What is value of applied force F for which the block remains at rest with respect to incline?

Statement-1: Systematic errors tend to occur in one direction, either positive or negative. Statement-2: Instrumental error, Random error, least count error, personal error are systematic error.

For what value of E will the potential of point A equal the potential of point B?