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A monkey of mass 20kg climbs on a rope which can stand a maximum tension of 300 N.in which of the following cases the rope breaks? The monkey

Options

Climbs up with an acceleration of 6m/s2

Climbs up with a uniform speed of 5m/s

Climbs down with an acceleration of 4m/s2

Falls down the rope nearly freely under gravity

Ans :1st option

If i start the chapter motion in one dimension not units and dimention first then i can face any problem?

A system is given $400\text{cal}$ of heat and $1000\text{J}$ of work done by the system, then the change in internal energy of the system will be

To which part of the electromagnetic spectrum does the Balmer series of Hydrogen belong?

Velocity of a particle is $\overrightarrow{v}=6\hat{i}+2\hat{j}-2\hat{k}$. The component of the velocity parallel to vector $a=\hat{i}+\hat{j}-\hat{k}$ in vector form is

Kirchhoff’s current and voltage law are based on:

Compass needle gives 20 oscillations in 1 minute at a point A, it gives 60 oscillations in 150 seconds at a point B, at A & B net field due to earth are in ratio of 4 : 3, find ratio of $cos\delta$ at both points $(\delta$ = angle of dial)

The equation of a plane progressive wave by y = 2 $sin(5\pi t-0.5\pi x)$. The speed of the wave [x and y are in metre and t is in second] is

Of the following particles, the one that can be added to the nucleus without changing its chemical properties is

A screw gauge with a pitch of $0.5\text{mm}$ and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5\text{mm}$ and the 25th division coincides with the main scale line?

An infinite line charge of uniform electric charge density $\lambda$ lies along the axis electrically conducting infinite cylindrical shell of radius $R.$ At time $t=0,$ the space in the cylinder is filled with a material of permittivity $\epsilon$ and electrical conductivity $\sigma .$ The electrical conduction in the material follows Ohm's law. Which one of the following best describes the subsequent variation of the magnitude of current density $j\left(t\right)$ at any point in the material?

A small sphere initially at rest, falls in to a viscous liquid. Due to drag, heat is produced. Then the relation between rate of production of heat and the radius of the sphere at terminal velocity, is best represented by:

L, C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?

A horizontal straight conductor of mass ‘m’ and length ‘l’ is placed in a uniform vertical magnetic field of magnitude ‘B’. An amount of charge ‘Q’ passes through the rod in a very short time such that the conductor begins to move only after all the charge has passed through it. Its initial velocity will be

The volume of a metal sphere increases by $0.15\%,$ when its temperature is raised by ${24}^{\circ }\text{C}$. The coefficient of linear expansion of metal is:

A T.V tower has a height of 100m. How much population is covered by the T.V broadcast if the average population density around the town is $1000/{\text{km}}^2$ ?

A spring block system is kept on a frictionless surface. Match the respective entries of column (I) with column (II) assuming minimum potential energy for the system as zero.
($K$ = Spring constant, $A$ = Amplitude, $m$ = Mass of block)
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) If mass of the block is doubled}& \text{(p) Time period increases}\\ \text{(keeping}K\text{,}A\text{unchanged)}& \\ \text{(B) If the amplitude of oscillation is doubled}& \text{(q) Time period decreases}\\ \text{(keeping}K\text{,}m\text{unchanged)}& \\ \text{(C) If force constant is doubled}& \text{(r) Energy of oscillation increases}\\ \text{(keeping}m\text{,}A\text{unchanged)}& \\ \text{(D) If another spring of same force constant}& \text{(s) Energy of oscillation decreases}\\ \text{is attached parallel to the previous one}& \\ \text{(keeping}m\text{,}A\text{unchanged)}& \text{(t) Energy of oscillation remain constant}\end{array}$

In the figure shown, the charge on the capacitor is $q=\left(4t^2\right)\text{C}$ then $V_{ab}$ at $t=1\text{s}$ is

If a body starts from rest and travels $120\text{cm}$ in the $6^{th}$ second, then the acceleration of the body is

Three rings each of mass $M$ and radius $R$ are arranged as shown. The moment of inertia of the system about $YY\text{'}$ will be

The coefficient of static and kinetic friction between a body of mass $m=1$ unit and the surface are $.75$ and $.50$ respectively. A force is applied to the body to maintain constant acceleration when the body is in motion. This constant force is:

Two blocks of mass $m_1$ and $m_2$ are connected by a weightless rod on a plane having inclination of ${37}^{\circ }$. The coefficients of dynamic friction of $m_1$ and $m_2$ with the inclined plane are $\mu =0.25$. Then the common acceleration of the two blocks and the tension in the rod are

A body is thrown horizontally with a velocity $\sqrt{2gh}$ from the top of the tower of height $h$. It strikes the level ground through the foot of the tower at a distance $x$ from the tower. The value of $x$ is

A smaller disc is removed from a uniform circular lamina as shown in the figure. Find the position of $COM$ of the uniform lamina, if diameter of the smaller disc is $12\text{m}$.

The each revolves round the sun due to gravit ational attraction. Suppose that the sun and the earth are point particles with their existing mas ses and that Bohr's quantization rule for angular momentum is vaild case of gravitation.

(a) Calculate the minimum radius the earth can have for its orbit.

(b) What is value of the principal quantum num ber n for the present radius ? Mass of the earth = $6.0\times {10}^{24}$ kg, Mass of the sun = $2.0\times {10}^{30}$ kg, earth-sun distance = $1.5\times {10}^{11}$ m.

A disc of mass 5kg and radius 50cm rolls on the ground with a velocity of 10m/s . Calculate the kinetic energy of disc ( I= MR²/2)

Find the acceleration of the block of mass M in the situation shown in figure. All the surfaces are frictionless and the pulleys and the string are light.

The velocity at the maximum height of a projectile is half of its initial velocity of projection . The angle of projection is?

The equation of a projectile is $y=ax-b{x}^2$. Its horizontal range is

Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are placed at rest on a frictionless surface and connected by a spring. An external hit gives a velocity of $21\text{m/s}$ to the heavier block towards the lighter one. Velocities of both blocks (heavier and lighter one) in the centre of mass frame, just after the kick will be respectively:
(Consider direction of motion of heavier block as $+ve$ direction)

The pulley shown in figure has moment of inertia $I=5{\text{kg-m}}^2$ about its axis and radius $R=1\text{m}$. Find the acceleration of the blocks if the masses of the blocks are $M=3\text{kg}$ and $m=2\text{kg}$. Assume that the string is light and does not slip on the pulley and $g=10{\text{m/s}}^2$.

If $\alpha \text{and}\beta$ are the roots of $x^2-5x+6=0$ then $\frac{1}{\alpha }+\frac{1}{\beta }$ is

Density of a mixture is $\rho$, when fluids of densities ${\rho }_1\text{and}{\rho }_2$ are mixed in the same proportion. Then:

Which of the following force is conservative force?

Two trains, A and B, each $50m$ long, are approaching a meeting point travelling with velocities $10m/s$ and $15m/s$ respectively. The tracks of the two trains are perpendicular to each other and both trains are $500$ meters away from the meeting point. How far will be the train A from meeting point when train B crosses the meeting point?

In a uniform circular disc angular velocity is constant .why?

The centre of mass of a system of three particles of masses $2\text{g},3\text{g}$ and $5\text{g}$ is taken as the origin of a co-ordinate system. The position vector of a fourth particle of mass $8\text{g}$, such that the centre of mass of the four particle system lies at the point $(3,4,7)\text{m}$, is $\lambda (3\hat{i}+4\hat{j}+7\hat{k})\text{m}$ where $\lambda$ is a constant. Find the value of $\lambda$.