A point objects of mass m is slipping down on a smooth hemispherical body of mass M and radius R. The point object is tied to a wall with an ideal string as shown. At a certain instant, speed of the hemisphere is v and its acceleration is a. Then speed v(p) and acceleration a(p) of a particle has value (Assume all the surfaces in contact are frictionless)

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t=0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t=0 along the horizontal string AB with speed v. Friction between the bead and the string may be neglected. Let t p and t Q be respective times taken by P and Q to reach point B,

[vc_row][vc_column][stm_post_info css=".vc_custom_1437111129257{margin-bottom: 0px !important;}"][vc_row_inner][vc_column_inner width="1/6"][/vc_column_inner][vc_column_inner width="1/6"][/vc_column_inner][/vc_row_inner][vc_row_inner][vc_column_inner width="1/6"][/vc_column_inner][vc_column_inner width="2/3"][vc_single_image image="134810" img_size="large"][vc_single_image image="134811" img_size="large"][/vc_column_inner][vc_column_inner width="1/6"][/vc_column_inner][/vc_row_inner][vc_row_inner][vc_column_inner width="1/2"][stm_post_tags][/vc_column_inner][vc_column_inner width="1/2"][stm_share code="JTNDc3BhbiUyMGNsYXNzJTNEJTI3c3RfZmFjZWJvb2tfbGFyZ2UlMjclMjBkaXNwbGF5VGV4dCUzRCUyNyUyNyUzRSUzQyUyRnNwYW4lM0UlMEElM0NzcGFuJTIwY2xhc3MlM0QlMjdzdF90d2l0dGVyX2xhcmdlJTI3JTIwZGlzcGxheVRleHQlM0QlMjclMjclM0UlM0MlMkZzcGFuJTNFJTBBJTNDc3BhbiUyMGNsYXNzJTNEJTI3c3RfZ29vZ2xlcGx1c19sYXJnZSUyNyUyMGRpc3BsYXlUZXh0JTNEJTI3JTI3JTNFJTNDJTJGc3BhbiUzRSUwQSUzQ3NwYW4lMjBjbGFzcyUzRCUyN3N0X3NoYXJldGhpc19sYXJnZSUyNyUyMGRpc3BsYXlUZXh0JTNEJTI3JTI3JTNFJTNDJTJGc3BhbiUzRQ=="][/vc_column_inner][/vc_row_inner][stm_post_author][stm_post_comments][/vc_column][/vc_row]

A disc of mass m and radius R lies flat on a smooth horizontal table. A mass less string runs halfway around it as shown in figure. One end of the string is attached to a small body of mass m and the other end is being pulled with a force F. The circumference of the disc is sufficiently rough so that the string does not slip over it. Find acceleration of the small body.

A smooth semicircular wire-track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R/4 is attached to the lowest point O of the wire-track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The ring is held staionary at point P such that the spring makes an angle of 60 with the vertical. The spring constant K=mg/R. Consider the instant when the ring is released, and (i) draw the free body diagram of the ring, (ii) determine the tangential acceleration of the ring and the normal reaction.