Tiêu đề IIT-JAM-PHYSICS-MECHANICS (PYQ's).pdf ✅

MECHANICS
DIMENSIONAL ANALYSIS 1 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 IIT-JAM-PHYSICS – 2024 ASSIGNMENT-1.1 : DIMENSIONAL ANALYSIS 1. Planck’s constant (h), the speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants of nature. Which of the following combinations has the dimensions of length? (a) 3/2 hG c/ (b) 5/2 hG c/ (c) hc G/ (d) 3 2 Gc h/ [JNU 2009] 2. If h is the Planck constant, c the speed of light in vacuum and G the universal gravitational constant, which of the following quantities has the dimension of length? [JNU 2014] (a) 2 hG c (b) 4 hG c (c) hc G (d) 5 hG c (e) 3 hG c 3. The heaviest pebble of mass m that can be moved by a stream is known to be proportional to some powers of the speed of the stream v, the density (of water)  and the acceleration due to gravity g. Using dimensional analysis, we may conclude that m is proportional to [JNU 2015] (a) 4 v g  (b) 5 2 v g  (c) 6 3 v g  (d) 3 4 v g  (e) 2 v g 4. Let us write down the Lagrangian of a system as L x x x  , ,     2 L x x x mxx kx cxx , ,        . What is the dimension of c? (a) 3 MLT (b) 2 MT  (c) MT (d) 2 1 ML T  5. A particle is confined to the region x  0 by a potential which increases linearly as 0 u x u x ( )  . The mean position of the particle at temperature T is (a) 0 B k T u (b) 2 0 ( ) B k T u (c) 0 B k T u (d) 0 B u k T 6. In the scattering of some elementary particle, the scattering cross-section  is found to depend on the total energy E and the fundamental constant h (Planck’s constant) and c (the speed of light in vacuum). Using dimensional analysis, the dependence of  on these quantities is given by (a) hc E (b) 3/2 hc E (c) 2       hc E (d) hc E 7. Using dimensional analysis, Planck defined a characteristic temperature TP from powers of the gravitational constant G, Planck’s constant h, Boltzmann constant B k and the speed of light c in vacuum. The expression for TP is proportional to (a) 5 2 B hc k G (b) 3 2 B hc k G (c) 4 2 B G hc k (d) 2 3 B hk Gc
DIMENSIONAL ANALYSIS 2 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 8. If the task of a given problem is to find a certain length, which of the following quantities could be the answer? (The l, v, a, t and m in this and the following two questions are given quantities with the dimensions of length, velocity, acceleration, time, and mass) (a) at (b) mvt (c) al (d) v t/ (e) 2 v a 9. If the task of a given problem is to find a certain time, which of the following quantities could be the answer? (a) a t (b) mv l (c) 2 v a (d) l a (e) v a 10. If the task of a given problem is to find a certain force (with units kgm/s2 ), which of the following quantities could be the answer ? (a) 2 mv (b) mat (c) mv/t (d) mv/l (e) 2 v l 11. A mass m oscillates back and forth on a spring with spring constant k (with units kgm/s2 ). If the amplitude (the maximum displacement) is A, which of the following quantities is the maximum speed the mass achieves as it passes through the equilibrium point ? (a) kA m (b) 2 kA m (c) kA m (d) 2 kA m (e) 2 mkA 12. It is required to construct the quantum theory of a particle of mass m moving in one dimension x under the influence of a constant force F. The characteristic length-scale in this problem is [TIFR 2015] (a)  mF (b) 1/3 2        mF (c) 1/3 2        m F (d) 2  mF ANSWER KEY 1. (a) 2. (e) 3. (c) 4. (c) 5. (a) 6. (c) 7. (a) 8. (e) 9. (d) 10. (c) 11. (d) 12. (b)
PROBLEM SOLVING STRATEGIES 3 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 IIT-JAM-PHYSICS – 2024 ASSIGNMENT-1.2 : PROBLEM SOLVING STRATEGIES 1. A person throws a ball (at an angle of her choosing, to achieve the maximum distance) with speed  from the edge of a cliff of height h. Assuming that one of the following quantities is the maximum horizontal distance the ball can travel, which one is it? (a) 2 2 gh  (b) 2 g  (c) 2 h g  (d) 2 2 2 1 gh g    (e) 2 2 2 1 gh g          (f) 2 2 / 2 1 g gh    2. A very long rod rotates about a pivot with a constant angular velocity . A bead is constrained to slide along the rod without friction. At time t = 0, the bead is at rest a distance d away from the pivot. Its distance r(t) from the pivot at time t is (a) dsinh t   (b) dsin t   (c) d cos h t   (d) d cos t   3. A ball is thrown at an angle  up to the top of a cliff of height L, from a point a distance from the base. Assuming that one of the following quantities is the initial speed required to make the ball hit right at the edge of the cliff, which one is it? (a) 2(tan 1) gL   (b) 1 cos 2(tan 1) gL    (c) 1 cos 2(tan 1) gL    (d) cos 2(tan 1) gL    4. A particle is projected vertically upward and it reaches the maximum height H in time T seconds. The height of the particle at any time t will be (a)   2 g t T (b)   1 2 2 H g t T   (c)   1 2 2 g t T (d) H g t T     5. Consider the “endcap” of the sphere shown in figure, obtained by Slicing the sphere with vertical plane perpendicular to the plane of the paper. Which of the following expressions is the volume of the cap? (a)   3   R 4 / 3 (2 / 3)sin  (b)   3   R (2 / 3)sin (c)   3    R 2 / 3 (2 / 3)cos sin   (d)   3 3    R 2 / 3 (1/ 3) cos cos  