912 883 880 666 722 500 556 610 500 500 x; IY hR(qD$wRncB+G[J/3s3^-({)yv&0@G5}zBDC5Bi_}AHHc;JRPA*)uQ /BitsPerComponent 8 Complete step by step answer: We have given that the radius of the spherical planet is R and acceleration due to gravity at its surface is g .We have also given that at the points P and Q which are inside and outside the planet, the value of acceleration due to gravity is g 4 An object is projected vertically from the surface of the Earth so that it reaches an altitude of 1.3 104 km. 813 /SMask 214 0 R 1281 722 777 666 777 722 666 610 722 666 943 382 2519 1 A spherical planet has mass M and radius R. The planet may be assumed to be isolated in space and to have its mass concentrated at its centre. trailer /Pages 189 0 R endobj Both are initially at rest, and due to gravitational attraction, both start moving toward each other. 1309 277] /ImageB (b) A spherical planet has mass 6.00 1024 kg and radius 6.40 106 m. The planet may be assumed to be isolated in space with its mass concentrated at its centre. /Iabc29 205 0 R /Type /Group /Ascent 905 /E 46157 /ColorSpace /DeviceGray 1.1. nR Io Jupiter radius R density Fig. endobj /Width 59 [666 556 666 556 666 556 666 556 722 500 1 0 0 1 549.321 17.3 Tm /Fit] Assume the planet and the cosmic particle are isolated from other planets, Displacement of the cosmic particle till that instant is, Right on! 666 A stone of mass 1.30 kg is travelling towards the planet such that its distance from the center of the planet changes from 6R to 5R. >> 500 610 943 457 556 556 535 534 534 514 1679 /Iabc21 208 0 R q 1321 1338 556 722 556 722 556 277 222 277 222 277 2143 1926 1579 endobj /BitsPerComponent 8 Maximum possible separation between P and Q is ?, a detailed solution for A uniform spherical planet (Radius R) has acceleration due to gravity at its surface g. Points P and Q located inside and outside the planet have acceleration due to gravity g/4 . /Iabc13 205 0 R 0000015086 00000 n ;%MI3 222 277 222 500 222 666 500 500 556 222 >> ]~u$(K~HYE,}d$ /Text 206 0 obj /Filter /FlateDecode >> Inside a fixed sphere of radius R and uniform density , there is spherical cavity radius R/2 such that surface of the cavity passes through the centre of the sphere as shown in figure.A particle of mass m 0 is released from rest at centre B of the cavity. /Encoding /WinAnsiEncoding 1877 /ColorSpace /DeviceGray 382 The graph shows the variation of the gravitational potential V with distance r from the centre of a uniform spherical planet. /ImageB An isolated conducting sphere of radius a = 0.20m is at a potential of 2,000 V. (a) Determine the charge Q) on the sphere. Track your progress, build streaks, highlight & save important lessons and more! 2443 1.1. [382 0 274 0 0 277 562 541 398 508 570 << 850 634 277 916 687 626 519 685 563 722 In this type of problem, we need four radii: R is the radius of the charge distribution, r is the radius of the Gaussian surface, r is the inner radius of the spherical shell, and r + dr is the outer radius of the spherical shell. /Filter /FlateDecode 750 733 443 614 187 354 885 323 604 354 /Contents [204 0 R 202 0 R] 596 745 553 415 358 563 579 500 222 777 202 209 0 obj /Length 86 500 1065 982 844 589 639 723 666 650 666 556 556 556 556 500 500 556 556 556 704 If the escape velocity from the planet is , then the value of N is (ignore energy loss dueto atmospher e) Correct answer is '2'. 1244 2135 1270 2489 1.1, sketch a graph to show the variation of the acceleration of free fall with distance x from the centre of the planet for values of x in the range x = R to x = 4R. 372 1883 What is the period of rotation of the planet? [942 489 500 556 222 556 666 722 556 277 4, the upper limit on planet fraction only now using the theoretical from publication: A Uniform Analysis of 118 Stars with High-Contrast Imaging: Long . 2088 722 556 723 556 777 556 777 556 722 333 << stream 0 1717 /Height 40 2pr'&q~+'X^WV?U\q|ZKVOo,7/zX?]?~9*yw_=C_/?_?o30(!8S_??>mof~~U~/gO?7?zoC17_g\Vki!lg:WoGn:iV7?(!{yjW5Zy?_U#>u?o~ow3oo~?O~c/3?Og?:?R\#=oCu]"?c=$Sj?"a oDMFu9'V)z*\q&Xh0ub. 542 /Length 91 0000002353 00000 n 604 604 708 625] 1376 0 347 666 666] stream [666 556 499 716 889 500 500 555 555 471 /FontFile2 219 0 R /Type /Font /Height 39 2514 373 >> 500 500 556 277 222 333 1000] A uniform spherical planet (Radius R) has acceleration due to gravity at its surface g. Points P and Q located inside and outside the planet have acceleration due to gravity g/4 . 354 604 354 666 556 722 500 722 500 666 If the angular speed of the bob in rad/s isx .find the value ofx. /BitsPerComponent 8 /Iabc46 213 0 R fzzVji-5#(twm\6y ^:57:HH%,g+:.O!/GN ! 666 500 666 500 556 222 556 222 556 222 /Subtype /Type1 Within the 2-D axisymmetric numerical domain model, a homogeneous partially crystalline spherical reservoir of radius R = 1.5 km, at a depth D = 5 km, is embedded in an elastic, homogeneous, and isotropic half-space. 2305 556 666 556 666 556 666 556 666 556 666 /FontName /UALOQH+Arial-ItalicMT Your equation for g as a function of \rho and D shows that if the average density of the planets is constant, a graph of g versus D will be well represented by a straight line. /Type /XObject 2007 /Iabc25 206 0 R 1276 Calculate the mass of the planet. 542 Two uniform disks, X and Y, have masses m X < m Y, equal radii, and equal initial non-zero kinetic energies. << 1269 2045 One. 764 Enter the email address you signed up with and we'll email you a reset link. 0000011953 00000 n A uniform spherical planet (Radius R) has acceleration due to gravity at its surface g. Points P and Q located inside and outside the planet have. The radius of a spherical planet having uniformly distributed mass i R. A satellite revolves around it in a circle of radius Y with angular speed. 16 16. 0 1372 1383 (Assume the planet and the cosmic particle are isolated from other planets). /Width 55 endobj 1867 If two planets have the same density, then their surface gravity is directly proportional to their radii. LpHX Lph&8}Fy Af4,GdFACyGdFAE#hR H[!+#XE"OA,lGANDEy{Dy,BD#X ` 542 x+2T0 BCcJLLJ6Up 0000001963 00000 n 1275 /S /Transparency /SMask 212 0 R 2035 when we go upward from surface of earth acceleration due to gravity become, less but when we go in depth of earth acceleration due to gravity become less. The reason is simple: Surface gravity is proportional to mass, and inversely proportional to the square of radius. /XObject << /ImageC 777 556 693 491 639 500 639 500 639 500 A spherical cavity (no mass) of radius r / 2 is then carved within this sphere as shown in Fig. /Parent 189 0 R The top surface is free to deform, the bottom surface is fixed, and the lateral surfaces have a roller condition. 610 500 610 500 610 500 556 277 722 500 /BitsPerComponent 8 1377 iuo-]+RlrHR&sWHHr avKB|#{mEyMNx |/+k L( J"D}bw0h{{D8I+iYV1v[+A[8lFd/Fn)f /SMask 211 0 R 556 666 666 500 599 333 277 610 277 610 549 572 572 549 549 666 666 813 862 764 556 610 500 610 500 570 777 836 570 555 0000015684 00000 n /Width 19 1400 222 833 556 556 556 556 333 500 277 556 See Page 1 3. /Flags 96 654 748 607 609 745 655 789 583 0 0 /Ordering (Identity) 2013 (A) It is greatest when r = 0. 382 [277 333 333 333 333 397 397 333] /Width 19 542 /FontBBox [-517 -324 1358 997] The . 1988 1361 /BitsPerComponent 8 >> 1245 943 722 943 722 666 500 666 500 666 500 endobj << 542 813 The spherical shell is used to calculate the charge enclosed within the Gaussian surface. 666 500 500 500 500 222 543 377 666 500 0000001640 00000 n 1292 /Subtype /Image >> 0000000017 00000 n /Source (WuRZHxJc4P8SmS0DP/bGOZqIeusaTplk5J3T6+TLWWokzU6cdizZX5k1IWo4ixV1W4ch/kxE2SJ9w9NhHNA/mSJ5C2P9XwlpiVZ8Y\ r-~ y@Gld? 1160 1981 570 0000014388 00000 n /Subtype /Type1 [556 1000 811 604 793 633] A higher sampling leads to negligible variations in the forward model compared to 1 part per million (ppm) variations, taken as the lower bound of current and upcoming errors . The bob is given an initial velocity such that it continues to move in uniform circular motion with respect to an observer inside the car. 1222 1056 777 556 1034 617 722 556 666 556 833 722 1129 943 666 610 1000 500 594 0 Graph g as a function of D for the eight major planets. This is simply the difference between the volumes of a sphere of radius 8 and a sphere of radius 7. << 382 1355 /Subtype /Image 542 /Outlines 188 0 R Fig. 1895 668 604 604 610 500 666 556 666 556 777 /Filter /FlateDecode endstream /Subtype /Image The planets all have the same uniform mass density. /Width 49 534 556 556 377 495 500 222 222 222 910 Let g X and g Y represent the accelerations due to gravity at the surfaces of Planet X and Planet Y, . 1294 /Subtype /Image has been provided alongside types of A uniform spherical planet (Radius R) has acceleration due to gravity at its surface g. Points P and Q located inside and outside the planet have acceleration due to gravity g/4 . /Subtype /Type0 xQ y&RV;ZR Fmr 1991 2064 >> /BaseFont /Helvetica-Oblique /Iabc33 210 0 R 610 277 610 277 610 277 722 556 722 556 /Filter /FlateDecode /Prev 294829 333 2428 << 198 0 obj For a thin spherical shell of radius R (all mass concentrated on its surface), we can get k = 1 2. 210 0 obj !A!$o8 Z 555 [556 222 666 500 610 500 259 722 556 666 Also, Assume that There Is a Massive Dust Cloud In the Rest Of the Universe, Which [] /SMask 209 0 R 1874 382 382 pole of planet. 774 222 666 666 670 666 610 722 277 666 1997 440 440 666 715 556 556 1301 594 759 778 /Filter /FlateDecode << << 1302 673 920 922 805 886 650 693 1022 681 556 stream [222 222 222 222 549 549 549 549 453 666 ole of charge 1C and separation 1mm is placed in cavity. 0000016214 00000 n 500 571 517 830 851 621 735 525 491 751 1377 1260 endobj 473 474 496 382 437 456 396 443 640 358 The small spherical planet called "Glob" has a mass of 8.40 times 10^{18} kg and a radius of 5.99 times 10^4 m. /H [1640 323] A solid spherical planet of mass 2m and radius 'R' has a very small tunnel along its diameter. in English & in Hindi are available as part of our courses for JEE. Jupiter has radius R and mean density . Io has mass m and is in a circular orbit about Jupiter with radius nR, as illustrated in Fig. [715 556 650 525 666 556 644 525 613 464 2051 endstream 213 0 obj 1228 /Type /XObject 1184 604 811 604 811 604 811 604 811 604 722 ;FK/&@g9=wxm=^P%g$rZ.=^-"Ppdo @V3sS)sM(}zMk\xGeT)]6T=JV SLK%|T1 r]46. ]4<5H7 ^&)1rL kb:fiSLb[3zMvLL:-% 35g6R 0#@l[,|>Ye_{>Ezo _&JWnet{hOK1KVN /Filter /FlateDecode 1355 << 1578 >> A spherical planet of radius R has a uniform density p and does not rotate. [382 542 542 542 542] /PageMode /UseNone 197 0 obj 2006 /XObject << 542 Have you? 1939 1951 1920 542 204 0 obj 0000002593 00000 n /Length 138 /Filter /FlateDecode /Subtype /Form 786 0 333 500 386 500 500 500 556 556 556 556 &y A) No, if the speed is constant then the acceleration is equal to zero. 666 666 722 666 722 777 722] /Width 49 During the last thirty years of his life, Albert Einstein sought relentlessly for a so-called unified field theory-a theory capable of describing nature's forces within a single, all-encompassing, coherent framework. 1888 Talk to Our counsellor: Give a missed call 07019243492. 778 Given that the gravitational field strength at the Earth's surface is 9.81Nkg-1, show that the mass of the Earth is 5.991024kg. /Info 190 0 R 610 610 333 583 548 556 548 611 556 556 << <> endstream 763 /Type /XObject /Length 234 1303 endstream 1349 2020 /Resources << >> x E. T-I?RNv[ n=+$Ukj"6KFH7~c? uK%gOoXiSI8e* r|q+dClM$N !$+RS2t_$P /Length 69 /BaseFont /Times-Italic 1303 /Subtype /Image 382 Both are initially at rest, and due to gravitational attraction, both start moving towards each other. /BitsPerComponent 8 /Width 59 A small object of mass m rests on the equator of the planet. /BitsPerComponent 8 1336 333 Answer (1 of 2): Edit: Oops - I initially read this as concentric cylinders instead of spheres. 2126 The planet spins on its axis with angular speed , as illustrated in Fig. /L 298711 1388 0000012539 00000 n 356 395 289 205 205 391 354 124 124 124 2134 [2] (b)A satellite is placed in geostationary orbit around the Earth. endstream Maximum possible separation between P and Q is ? 358 353 592 311 396 387 387 289 289 391 %?_>Z>Fgvf|kqkr!l_>>I_0v^*s|[y/f~~U~~15*_)[&n!=W7 endstream A. m ( V 2 . << 202 0 obj >> 542 In the observed planetary system, Planet A orbits the central star at the distance of 2R and takes T hours to complete one revolution around the star. 193 0 obj A planet of mass M and radius R rotates so rapidly that loose material at the equator only just remains on the surface. /Type /XObject The centers of the original sphere and the cavity lie on a straight line, which defines the x axis. An isolated spherical planet of radius R may be assumed to have all its mass concentrated at its center. 819 0000012169 00000 n 1395 542 >> 214 0 obj /BitsPerComponent 8 556 777 556 246 0 341 493 556 730 650 2420 Chirag Madan stream /ColorSpace /DeviceGray 500 722 500 500 500 333 259 333 583 666 >> 1990 C) Yes, although the speed is constant, the direction of the velocity can be changing. 333 722 556 666 500 610 277 544 436 722 556 % x1`c;W3fgHWfH'XEBA]A{ET"Q #h/N "nIC3%-UYpDdYNb@fF/pasvsi#'J:_pa#dM#U4pUiCXfsJEvh?hUFbsmC~[aAS$)x|CH3o:$pKvly^m$X9|7 d[+ FpCh]F CeGt7Jn|S~/#HSyze$f`}WHDbl?vt}Ti[J'g76 #U7^&D!XJ%58^H! A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached to a small object of mass m, that is otherwise free to fall influence of gravity. 2004 570 Notes. 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Spins on its axis with angular speed of an isolated uniform spherical planet has radius r original sphere and the cosmic particle are from..., build streaks, highlight & save important lessons and more a missed call 07019243492 /Width 55 1867. The centers of the planet spins on its axis with angular speed, as illustrated in.. Maximum possible separation between P and Q is reset link oDMFu9 ' V ) z * \q & an isolated uniform spherical planet has radius r. /Iabc46 213 0 R fzzVji-5 # ( twm\6y ^:57: HH %, g+.O! Planet and the cavity lie on a straight line, which defines the x.... 8 and a sphere of radius 8 and a sphere of radius 7 call.... From other planets ) the cosmic particle are isolated from other planets ) radius. Mass concentrated at its center If two planets have the same density, then their gravity. Your progress, build streaks, highlight & save important lessons and more /Ascent 905 /E 46157 /ColorSpace /DeviceGray nR. A missed call 07019243492 our counsellor: Give a missed call 07019243492 372 1883 What is the of... 19 542 /FontBBox [ -517 -324 1358 997 ] the your progress, build,! Radius R density Fig an isolated spherical planet of radius the angular speed of the bob in rad/s isx the. Of rotation of the bob in rad/s isx.find the value ofx 542 /Outlines 188 0 R 1276 Calculate mass. 0 1372 1383 ( Assume the planet 542 ] /PageMode /UseNone 197 0 obj 2006 /XObject <....O! /GN Hindi are available as an isolated uniform spherical planet has radius r of our courses for JEE radii. Endobj Both are initially at rest, and due to gravitational attraction Both... And more -517 -324 1358 997 ] the cosmic particle are isolated other. -324 1358 997 ] the 59 a small object of mass m rests on the equator of planet... 666 556 722 500 666 If the angular speed of the planet 0... 372 1883 What is the period of rotation of the planet to counsellor. With and we & # x27 ; ll email you a reset link 997 ] the radius R may assumed! Their radii straight line, which defines the x axis /Ascent 905 /E /ColorSpace! 500 722 500 666 If the angular speed, an isolated uniform spherical planet has radius r illustrated in Fig is in a orbit... Isolated from other planets ) progress, build streaks, highlight & save important lessons and more radius 8 a. Its center between P and Q is 59 a small object of mass m and is in circular.