List of practice Questions

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. The orbital velocity of a satellite orbiting at an altitude of half of the radius, is

A particle is revolving in a circle of radius $R$. If the force acting on it is inversely proportional to $R$, then the time period is proportional to

$1 \,Kcal$ of heat flowing through a rod of iron. When the rod is cut down to $4$ pieces then what will be the heat flowing through each piece having same differential temperature?

Speed in kilometer per hour in S.I. unit is represented as

S.I. unit of velocity is

If the potential energy of a body on a planet is numerically $U$ and the escape velocity for the same body be $v_{e}$ for the same planet then $U / v_{e}$ will be :

A car of mass $ m $ moves in a horizontal circular path of radius $ r $ meter. At an instant its speed is $ v\,m/s $ and is increasing at a rate a $ m/s^{2} $ , then the acceleration of the car is:

An object of mass $40\, kg$ and having a velocity $4\, m/s$ collides with another object $ \left( m=60\,kg \right) $ having velocity $2\, m/s$. The collision is perfectly inelastic. The loss in energy is:

An iron rod of length $2 \,m $ and area of cross-section $ 50\,mm^{2}$ stretches by $ 0.5\,mm $ , when a mass of $250\, kg$ is hung from its lower end. The Young's of iron rod is:

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $ 1\,m/s $ , so as the have same kinetic energy as that of the boy. The original speed of the man is:

An earth satellites $ S $ has an orbit radius which is $4$ times that of communication satellite $C$. The period of revolution of $ S $ will be:

$ n $ small balls, each of mass $ m $ impinge elastically each second on a surface with a velocity $ u $ , then the force experienced by the surface in one second, will be:

Dimensions of surface tension are:

A wet open umbrella is held vertical and it whirled about the handle at a uniform rate of $21$ revolutions in $44\, s$. If the rim of the umbrella is a circle of $1\, m$ in diameter and the height of the rim above the flour is $4.9\, m$, the locus of the drop is a circle of radius:

The moment of inertia of a body about a given axis is $1.2 \,kg - m ^{2}$. To produce a rotational kinetic energy of $1500\, J$ an angular acceleration of $25\, rad / s ^{2}$ must be applied for :

The reaction of propene with HOCl proceeds via the addition of

The number of S - S bonds in sulphur trioxide trimer, $(S_3O_9)$ is

The correct order of equivalent conductance at infinite dilution of $LiCl, NaCl $ and $KCl $ is

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

If the positive numbers a,b,c,d are in AP. Then, $abc, abd, acd, bcd $ are

In the binomial expansion of $(a - b)^n , n \ge 5 $ the sum of the 5th and 6th terms is zero. Then, a /b equals

Let AB be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then, the locus of the centroid of the $\Delta PAB$ as P moves on the circle, is

Let $ \alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $y, \delta$ be the roots of $x^2 - 4x + q = 0$ if $ \alpha, \beta, y \delta$ are in GP, then the integer values of p and q respectively are

In a solid $'AB'$ having the $NaCl$ structure, $'A'$ atoms occupy the corners of the cubic unit cell. If all the face centred atoms along one of the axes are removed, then the resultant stoichiometry of the solid is