A particle of mass 0.3 kg starts moving from rest, in one dimension, under a force that delivers constant power $\mathrm{P}=1.5$ watt. The kinetic energy of the particle will be $\mathrm{KE}=15$ Joule after a time of
A trolley of mass 200 kg carrying a sandbag of mass 20 kg is moving on a frictionless horizontal track with speed $36 \mathrm{ km} / \mathrm{hr}$. After a while, sand starts leaking out of the bag on the floor of trolley at the rate $0.04 \mathrm{ kg} / \mathrm{sec}$. What is the speed of trolley after the entire sand bag is empty?
A particle, initially at rest at origin, starts moving under acceleration $a$ along +x direction. The acceleration versus time graph is shown in figure. The displacement and the velocity of the particle after 6 second are
Gravitational potential energy of a system of two particles of masses $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$, separated by distance r , is given by $\mathrm{U}=-\frac{\mathrm{Gm}_{1} \mathrm{ m}_{2}}{\mathrm{r}}$, where G is the universal Gravitational constant. Consider two stars, each of mass M , initially separated by distance d and at rest with respect to each other. The two stars start moving towards each other under their mutual gravitational attraction. The stars can be treated as point objects and motion is assumed non-relativistic. As measured from the laboratory frame, the speed of each star when they are at a distance $\frac{d}{2}$ apart from each other is
An engine approaches a vertical cliff with constant speed $72 \mathrm{ km} /$ hour . When the engine is at a distance of 0.7 km from the cliff, it blows a whistle. The driver hears the echo after a time (Speed of sound in air is $330 \mathrm{ m} / \mathrm{s}$.)
A vessel contains a liquid-1 of density $0.8 \mathrm{gm} / \mathrm{cm}^{3}$ over a liquid-2 of density $13.6 \mathrm{gm} / \mathrm{cm}^{3}$. The two liquids are immiscible. A homogeneous solid sphere floats with half of its volume immersed in liquid-1 and other half in liquid-2. The density of the material of the sphere in gm/ $\mathrm{cm}^{3}$ is
One fine morning, Mr. Ravi visited Gandhi park with his grandson. When he was just on a bridge over the lake in the park, an old wooden toy 'just' dropped from his hand. The toy went straight down to hit surface of calm water, then sinked into water to a certain depth below water surface and returns back due to upthrust of water to the hands of Mr. Ravi in the same position from where it was dropped. Assuming this position to be at height 19.6 meter above the surface of water, and density of material of toy to be just half the density of water in lake, the total time in which toy is received back to the hand of Mr. Ravi is calculated to be
Two plane mirrors OA and OB are inclined at an angle $\theta$ as shown in figure. A ray of light incident parallel to BO strikes the mirror OA at point P . It gets reflected from mirror OA and then reflected from the mirror OB , the ray finally emerges parallel to OA . The value of angle $\theta$ is
A long solenoid of length 2 m and radius 10 cm having 2000 turns per meter carries a current of 1.0 A . The strength of magnetic field (B) is maximum at point
A tank with a square base of area 2.0 meter $^{2}$ is divided by a vertical partition in the middle. The bottom of the partition has a small hinged door of area $10 \mathrm{ cm}^{2}$. The tank is filled with water in one compartment and a liquid of relative density 1.8 in other compartment, both to a height 5.0 meter. The force necessary to keep the door close is approximately $\left(\mathrm{g}=9.8 \mathrm{ m} / \mathrm{s}^{2}\right)$
An electron is projected horizontally towards east in uniform magnetic field B . The electron is deflected towards north by the magnetic field. The magnetic field is directed
Sir CV Raman announced the discovery of Raman Effect on February 28, 1928. He received 1930 Nobel Prize in Physics for this discovery. Raman Effect is the discovery of
Figures (i) to (v) show graphical representation of motion in one-dimension. Here $s, v, a$ and $t$ represent the displacement, the velocity, the acceleration and the time respectively.
Which of the above graphs represent uniform motion?
Three identical electric bulbs $\mathrm{A}, \mathrm{B}$ and C having specification 60 W , 220 V are connected across a 220 V supply as shown. The total power dissipated in three bulbs is close to
A copper wire is stretched to decrease its radius by $0.15 %$. The percentage change in the resistance of wire is
Speed of sound in air is directly proportional to square root of absolute temperature of air (keeping other parameters constant). The speed of sound in air at 273 K and 1 atom is $332 \mathrm{ m} / \mathrm{s}$. On a clear day, when temperature in the laboratory was $27^{\circ} \mathrm{C}$, an experiment was performed to measure speed of sound in air in the laboratory. The measured value comes out to be $352 \mathrm{ m} / \mathrm{s}$. the percentage error in this measurement is
ANY NUMBER OF OPTIONS 4, 3, 2 or 1 IN THE FOLLOWING QUESTIONS MAY BE CORRECT.
Two blocks $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ of masses 3 kg and 6 kg respectively are connected through a string and spring balance $\mathrm{B}_{1}$. The string passes over a massless and frictionless pulley P . The pulley is suspended from a rigid support through spring balance $\mathrm{B}_{2}$. Strings are massless and inextensible. Masses of spring balances are negligible. The system is released from rest. At the instant when masses $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ are moving with same speed ( $\mathrm{g}=9.8 \mathrm{ m} / \mathrm{sec}^{2}$ )
Focal length of a thin convex lens is 10 cm . An object is placed at a distance 15 cm in front of the lens and a plane mirror is kept at 20 cm on the other side as shown in figure.
Given network of 18 resistors, each equal to $\mathrm{R}=3$ ohm, is connected in series with resistor $\mathrm{R}_{0}$ to a source of $\mathrm{emf}=9$ volt. Choose the correct option.
Two bodies of masses $\mathrm{m}_{1}=2 \mathrm{ kg}$ and $\mathrm{m}_{2}=1 \mathrm{ kg}$ are moving towards each other in the same straight line with speed $12 \mathrm{ m} / \mathrm{s}$ and $6 \mathrm{ m} / \mathrm{s}$ respectively as shown in figure. The bodies can be assumed as point masses. After some time, the two bodies undergo elastic collision. After the collision
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.