List of practice Questions

A thin uniform rod ''AB'' of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity the rod, when its end B strikes the floor is (g is acceleration to gravity)
A thin tube of uniform cross-section is sealed at both ends. When it lies horizontally, the middle $5\, cm$ length contains mercury and the two equal ends contain air at the same pressure $P$. When the tube is held at an angle of $60^{\circ}$ with the vertical, then the lengths of the air columns above and below the mercury column are $46\, cm$ and $44.5\, cm$ respectively. Calculate the pressure $P$ in cm of mercury. The temperature of the system is kept at $30^{\circ}C$.
A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane ahout an axis passing through its centre and perpendicular to the plane with an angular velocity $\omega$ Another disc of same mass hut half the radius is gently placed over it coaxially. The angular speed o f the composite disc will be
A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal haves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T then $\frac{T}{T}$ is.
A thin rod of mass $m$ and length $2l$ is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from $0$ to $\omega$ in time $t$, the torque acting on it is
A thin circular ring of area A is perpendicular to uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of circuit is R. When.the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is
A thin convex lens of focal length 10 cm and a thin concave lens of focal length 20 cm are in contact. The combination acts as:
A thin glass (refractive index $1.5$) lens has optical power of $-8\, D$ in air. Its optical power in a liquid medium with refractive index $1.6$ will be
A tensile force of $2\times10^5$ dynes doubles the length of an elastic cord whose area of cross section is 2scm Young's modulus of the material of the cord is
A teaparty is arranged for 16 people along two sides of a large table with 8 chairs on each side. Four men want to sit on one particular side and two on the other side. The number of ways in which they can be seated is
A system has internal energy equal to $E_1$, 450 J of heat is taken out of it and 600 J of work is done on it. The final energy of the system will be
A suspension of $Ca(OH)_2$ in water is called
$A$ system absorbs $50 \,kj$ heat and does $20\, kj$ of work. What is the net change in the internal energy of the system?
A structural steel rod has a radius of 10 mm and a length of 1 m. A 100 kN force stretches it along its length. The strain on the rod is $(Y_{steel} = 200 ? 10^9 \,N \,m^{-2})$
A student has to answer $10$ questions, choosing atleast $4$ from each of parts $A$ and $B$. If there are $6$ questions in Part $A$ and $7$ in Part $B$, in how many ways can the student choose 10 questions ?
A student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which be can select a book is $255$, then the value of $n$ equals to
A string of length $l$ fixed at one end carries a mass m at the other end. The string makes $ \frac{ 2}{ \pi } $ rev/s around the horizontal axis through the fixed end as shown in the figure, the tension in the string is
A string of length l hangs freely from a rigid support. The time required by a transverse pulse to travel from bottom to half length of the string is
A strong magnetic field is applied on a stationary electron. Then the electron
A straight wire (conductor) of length 10 cm is kept in a uniform magnetic field of induction 0.02 T. The angle between the conductor and the-field direction is 30. A current of 5A is passed through the conductor. The force on the conductor is (in N)
A stream of water flowing horizontally with a speed of $15 m \,s^{-1}$ gushes out of a tube of cross-sectional area $10^{-2}$ $m^{2}$, and hits a vertical wall normally. Assuming that it does not rebound from the wall, the force exerted on the wall by the impact of water is
A stretched string of length $l$, fixed at both ends, can sustain Stationary waves of wavelength of wavelength $\lambda,$ correctly given by
A straight line is such that the sum of the reciprocals of its intercepts on the axes is K.Then it passes through the fixed point with co-ordinates
A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is
A stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making n rev/min. The total tension in the string when the stone is at the lowest point is