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68 quizzes
A satellite moves eastwards in a circular orbit of radius 2R in the plane of the equator, where R = 6400 km is the Earth's radius. Take g = 10 m/s² at the Earth's surface, and the Earth to turn once (eastwards) in 24 h. How often does the satellite pass straight over a given point on the equator? New
High School (11–12) · Gravitation
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Advanced
Which line of He⁺ has the same wavelength as the first Balmer line of hydrogen, n = 3 → 2?
High School (11–12) · Light, Atomic Spectra and the Bohr Model
JEE Main, NEET, BITSAT, WBJEE, Board Exam
StemPy LabStemPy Lab
Hard
A satellite of mass 1000 kg moves in a circular orbit of radius 2R round the Earth, where R = 6400 km is the Earth's radius. How much energy must be supplied to move it into a circular orbit of radius 4R? Take g = 10 m/s² at the Earth's surface. New
High School (11–12) · Gravitation
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
A thin uniform ring of mass 6.0 × 10²⁰ kg and radius R = 100 km floats in space, far from other bodies. A small rock is released from rest on the ring's axis, at a distance √3 R from its centre O, as shown in the figure. Take G = 6.67 × 10⁻¹¹ N m²/kg². With what speed does the rock pass through O? New
High School (11–12) · Gravitation
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
A uniform rod of length 0.90 m is held horizontal and dropped from rest, without turning. After it has fallen 0.45 m, its left end strikes a fixed sharp edge and is caught there, so that the rod starts to turn about the edge, as shown in the figure. Take g = 10 m/s². What is the angular speed of the rod just after the impact? New
High School (11–12) · Rotational Motion
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Advanced
A small bead of mass 0.20 kg is threaded on a smooth circular ring of radius 0.50 m, fixed in a vertical plane. A light spring of force constant 4.0 N/m, whose natural length equals the radius of the ring, has one end fixed at the top A of the ring and the other end tied to the bead. The bead is released from rest at P, level with the centre O, as shown in the figure. Take g = 10 m/s². What is the force from the ring on the bead when the bead passes the lowest point B? New
High School (11–12) · Work, Energy and Power
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
A block of mass 1.0 kg hangs at rest from a fixed point on a light string of length 0.80 m. A bullet of mass 20 g, moving horizontally, passes straight through the block and comes out with one third of its speed, as shown in the figure. The block is hardly changed by the hole. Take g = 10 m/s². What is the least speed of the bullet for which the block goes right round a vertical circle? New
High School (11–12) · Momentum and Collisions
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
A uniform chain of length 2.0 m and mass 2.0 kg lies on a rough horizontal table, with 0.5 m of it hanging over a smooth, rounded edge, as shown in the figure. The coefficient of friction between the chain and the table is 0.2. The chain is released and slides off. Take g = 10 m/s². What is its speed at the moment the last link leaves the table? New
High School (11–12) · Work, Energy and Power
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Advanced
A uniform rope of mass 0.40 kg and length 1.0 m lies on a smooth horizontal table. One end is tied to a vertical axle, and a small bead of mass 0.20 kg is fixed to the other end. The axle turns, and the rope and bead go round in a straight line at a steady 5.0 rad/s, as shown in the figure. What is the tension in the rope at its midpoint? New
High School (11–12) · Circular Motion
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
A uniform chain of length 2.0 m and mass 4.0 kg lies partly on a rough horizontal table, and the rest hangs over a smooth, rounded edge, as shown in the figure. The coefficient of sliding friction between the chain and the table is 0.2. The chain is sliding off the table. At the instant when 0.8 m of it hangs, what is the tension in the chain at the edge of the table? Take g = 10 m/s². New
High School (11–12) · Friction
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
A light rope passes over a light, smooth pulley fixed to the ceiling. A 50 kg crate is tied to one end of the rope and rests on the floor. A 40 kg monkey holds the other end, as shown in the figure, and starts to climb with an acceleration of 5 m/s² relative to the rope. Take g = 10 m/s². What is the acceleration of the crate? New
High School (11–12) · Newton's Laws of Motion
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Advanced
A block of mass 5 kg rests on a rough incline that makes 37° with the horizontal. The coefficient of friction is 0.75, both for sticking and for sliding. A force F, pointing up the incline at an angle φ above its surface, is to drag the block up the incline at a steady speed, as shown in the figure. Take g = 10 m/s², sin 37° = 0.6 and cos 37° = 0.8. What is the smallest force that can do this, and at what angle must it act? New
High School (11–12) · Friction
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
A car starts from rest on a flat circular track of radius 50 m. It speeds up along the track with a steady tangential acceleration of 3.0 m/s². The coefficient of static friction between the tyres and the road is 0.50. Take g = 10 m/s². How far along the track does the car go before its tyres begin to skid? New
High School (11–12) · Circular Motion
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Advanced
A steel wire 20 m long hangs down a mine shaft under its own weight. By how much does it stretch? (Density of steel 7800 kg/m³, Y = 2.0 × 10¹¹ Pa, g = 9.8 m/s².) New
High School (11–12) · Elasticity and Mechanical Properties of Solids
JEE Main, NEET, BITSAT, WBJEE, Board Exam
StemPy LabStemPy Lab
Hard
A body falls from rest from a height R above the Earth's surface. Ignoring air, how fast does it hit the ground? (g = 9.8 m/s², R = 6.4 × 10⁶ m.) New
High School (11–12) · Gravitation
JEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB
StemPy LabStemPy Lab
Hard
1.0 mol of a monatomic gas is mixed with 1.0 mol of a diatomic gas. What is γ for the mixture? New
High School (11–12) · Thermodynamic Processes and Specific Heats of Gases
JEE Main, NEET, BITSAT, WBJEE, Board Exam
StemPy LabStemPy Lab
Hard
A cup of soup cools from 80 °C to 70 °C in 5.0 minutes in a room at 20 °C. Using the average temperature in each interval, how long does it take to cool from 70 °C to 60 °C? New
High School (11–12) · Heat Transfer
JEE Main, NEET, BITSAT, WBJEE, Board Exam
StemPy LabStemPy Lab
Hard
A 40 g ice cube at 0 °C is put into 0.25 kg of juice (treat it as water) at 30 °C. What is the final temperature once the ice has melted? (Latent heat of fusion 3.34 × 10⁵ J/kg, c = 4186 J kg⁻¹K⁻¹.) New
High School (11–12) · Calorimetry and Change of State
JEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB
StemPy LabStemPy Lab
Hard
A pendulum clock with a steel rod keeps correct time at 20 °C. How many seconds does it lose in a day at 40 °C? (α = 1.2 × 10⁻⁵ K⁻¹; T ∝ √L.) New
High School (11–12) · Temperature and Thermal Expansion
JEE Main, NEET, BITSAT, WBJEE, Board Exam
StemPy LabStemPy Lab
Hard
A glass flask of 100 cm³ is filled to the brim with mercury and heated by 50 K. How much mercury spills? (γ of mercury 1.8 × 10⁻⁴ K⁻¹; α of glass 0.9 × 10⁻⁵ K⁻¹.) New
High School (11–12) · Temperature and Thermal Expansion
JEE Main, NEET, BITSAT, WBJEE, Board Exam
StemPy LabStemPy Lab
Hard
Taking g = 10 m/s², water leaves a small hole 1.25 m below the surface of a tank, moving sideways. The hole is 5.0 m above the ground. How far from the tank, in metres, does the jet land? New
High School (11–12) · Fluid Flow, Bernoulli's Principle and Viscosity
JEE Main, NEET, BITSAT, WBJEE, Board Exam, AP
StemPy LabStemPy Lab
Medium
A copper ball sits in oil inside a cylinder closed by a piston of area 0.010 m². A 200 kg mass is placed on the piston. By what fraction of itself does the ball's radius shrink? (Bulk modulus of copper 1.4 × 10¹¹ Pa, g = 9.8 m/s².) New
High School (11–12) · Elasticity and Mechanical Properties of Solids
JEE Main, NEET, BITSAT, WBJEE, Board Exam
StemPy LabStemPy Lab
Hard
A 600 kg weather satellite is boosted from a circular orbit of radius 2R to a wider circular orbit of radius 3R. What is the least energy its engines must supply? (g = 9.8 m/s², R = 6400 km.) New
High School (11–12) · Gravitation
JEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB
StemPy LabStemPy Lab
Hard
A probe is fired straight up from the Earth's surface at 8.0 km/s. Ignoring air, how high does it rise? (g = 9.8 m/s², R = 6.4 × 10⁶ m.) New
High School (11–12) · Gravitation
JEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB
StemPy LabStemPy Lab
Hard
A solid cylinder is let go on a rough slope at angle θ. What is the least coefficient of static friction for it to roll without slipping? New
High School (11–12) · Rotational Motion
JEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, IB
StemPy LabStemPy Lab
Hard
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