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39 quizzes
A thin uniform spherical shell has mass M, radius R and centre O. A particle of mass m is held inside it, at a distance R/2 from O, as shown in the figure. Take the gravitational potential to be zero far away. Which of the following statements are correct? New
High School (11–12) · Gravitation
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
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 planet moves round the Sun in an ellipse of eccentricity 0.50, with a period of 12 years. B and B' are the two ends of the minor axis, and P is the point nearest the Sun, as shown in the figure. How long does the planet take to go from B to B' through P? New
High School (11–12) · Gravitation
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
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 spherical shell has mass M, radius R and centre O. A small hole is cut in it at a point H, as shown in the figure. Which of the following statements are correct? New
High School (11–12) · Gravitation
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
Three stars, each of mass 2.0 × 10³⁰ kg, sit at the corners of an equilateral triangle of side 1.0 × 10¹¹ m. They move together in one circle round the centre of the triangle, under their own gravity alone, so that the triangle keeps its shape, as shown in the figure. Take G = 6.67 × 10⁻¹¹ N m²/kg². What is the period of their motion? New
High School (11–12) · Gravitation
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A small moon goes round a planet in a circular orbit with a period of 32 days. Suppose the moon were suddenly stopped in its orbit. Treating the planet and the moon as points, how long would the moon take to fall into the planet? New
High School (11–12) · Gravitation
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
Treat the Earth as a uniform sphere of radius R = 6400 km, with g = 10 m/s² at its surface, and take the gravitational potential to be zero far away. Which of the following statements are correct? New
High School (11–12) · Gravitation
JEE Advanced
StemPy LabStemPy Lab
Hard
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
A satellite moves in a circular orbit of radius r round a planet. Its rocket fires for a very short time along its direction of motion and raises its speed by 10%. Which of the following statements are correct? New
High School (11–12) · Gravitation
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A uniform rod of mass 2.0 kg and length 1.0 m is hinged at one end to a wall, so that it can turn freely in a vertical plane. It is held horizontal and then released, as shown in the figure. Take g = 10 m/s². Which of the following statements are correct? New
High School (11–12) · Rotational Motion
JEE Advanced
StemPy LabStemPy Lab
Advanced
A uniform solid cylinder rolls without slipping at 4.0 m/s along a rough level floor. Ahead, the floor joins smoothly onto a ramp whose surface has no friction at all, as shown in the figure. The cylinder goes up the ramp, comes back down, and returns onto the rough floor. What is its velocity once it again rolls without slipping on the floor? New
High School (11–12) · Rotational Motion
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A puck of mass 0.50 kg moves in a circle of radius 0.80 m at 2.0 m/s on a smooth horizontal table. It is held by a light string that runs to the centre of the circle and down through a small hole there. The string is pulled down slowly from below until the radius is 0.40 m, as shown in the figure. Which of the following statements are correct? New
High School (11–12) · Rotational Motion
JEE Advanced
StemPy LabStemPy Lab
Hard
A uniform rod of mass 2.0 kg and length 1.2 m stands upright on a smooth horizontal floor. It is disturbed very slightly and falls over, as shown in the figure. Take g = 10 m/s². Which of the following statements about the instant just before the rod lands flat on the floor are correct? New
High School (11–12) · Rotational Motion
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A uniform rod of mass 1.0 kg and length 1.0 m lies at rest on a smooth horizontal table. A sharp blow with an impulse of 2.0 N s is given to one end, along the table and at right angles to the rod, as shown in the figure (a view from above). What is the velocity of the other end of the rod just after the blow? New
High School (11–12) · Rotational Motion
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A billiard ball is a uniform solid sphere of radius 3.0 cm, at rest on a table. A cue held horizontally gives it a sharp, short blow in a vertical plane through its centre, at a height h above the table, as shown in the figure. For what value of h does the ball roll without slipping straight away, so that friction from the table plays no part at all? New
High School (11–12) · Rotational Motion
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A uniform solid sphere, a uniform solid disc and a thin ring, all of the same radius, are released from rest side by side at the top of a rough incline at 37°. Each has its axis horizontal and across the incline. The coefficient of friction between each body and the incline is 0.10. Take g = 10 m/s², sin 37° = 0.6 and cos 37° = 0.8. Which of the following statements are correct? New
High School (11–12) · Rotational Motion
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
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 yo-yo is a uniform solid disc of mass m and radius R, with a light string wound round its rim. A hand holds the free end of the string and moves it vertically so that the centre of the yo-yo stays at rest in the air while the yo-yo spins faster and faster, as shown in the figure. Take g = 10 m/s². What must the acceleration of the hand be? New
High School (11–12) · Rotational Motion
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A block of mass 2.0 kg slides at 5.0 m/s on a smooth floor and hits a block of mass 3.0 kg at rest, head-on. Which of the following statements are correct? New
High School (11–12) · Momentum and Collisions
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
A force F = (y i + 2x j) N, where x and y are the coordinates in metres, acts on a particle. The particle moves from the origin O to the point P (2 m, 2 m) along the parabola y = x²/2, as shown in the figure. How much work does the force do? New
High School (11–12) · Work, Energy and Power
JEE Advanced
StemPy LabStemPy Lab
Advanced
Ball A of mass 0.5 kg slides at 4.0 m/s on a smooth floor towards ball B of mass 1.5 kg, which is at rest. Beyond B there is a fixed wall, at right angles to the motion, as shown in the figure. All collisions are head-on and elastic. Which of the following statements are correct? New
High School (11–12) · Momentum and Collisions
JEE Advanced
StemPy LabStemPy Lab
Advanced
Two blocks, of masses 2.0 kg and 3.0 kg, rest on a smooth floor, joined by a light spring of force constant 100 N/m at its natural length. A constant horizontal force of 15 N starts to pull the 3.0 kg block away from the other one, as shown in the figure. What is the largest stretch of the spring? New
High School (11–12) · Work, Energy and Power
JEE Advanced, Olympiad
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
Two blocks, of masses 1.0 kg and 3.0 kg, lie on a smooth floor, joined by a light spring. The 1.0 kg block touches a fixed wall. The 3.0 kg block is pushed towards the wall, squeezing the spring by 0.20 m, and then released from rest, as shown in the figure. What is the largest stretch of the spring in the motion that follows? New
High School (11–12) · Momentum and Collisions
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
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