The torque due to the force (2 i+ j+2 k ) about the origin, acting on a particle whose position vector is ( i+ j+ k ), would be
(2) i- k
= r F= vmatrix i& j& k\\1&1&1\\2&1&2 vmatrix= i(2-1)- j(2-2)+ k(1-2)
= i- k
Answer: (2)
A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time t=0 the cylinder has a translational velocity v0=49 m/s, perpendicular to its axis and a rotational velocity v0/4R about the centre. The time taken by the cylinder to start rolling is seconds. (coefficient of kinetic friction K=0.25 and g=9.8 m/s2)
A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are and respectively.
The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point (p) of normal bisector, as shown in the figure is . [figure]
A solid sphere (A) of mass 5m and a spherical shell (B) of mass m, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of aA and aB, respectively. The ratio of aA and aB is .
Two identical bodies A and B of equal masses have initial velocities v1=4 i m/s and v2=4 j m/s respectively. The body A has acceleration a1=6 i+6 j m/s2 while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in path.
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle 1 and in the next 2 s it rotates through an angle 2. The ratio 2 1 is .
An object of uniform density rolls up the curved path with the initial velocity v0 as shown in the figure. If the maximum height attained by an object is 7v0210g (g = acceleration due to gravity), the object is a . [figure]
A solid sphere of mass M and radius R is divided into two unequal parts. The smaller part having mass M/8 is converted into a sphere of radius r and the larger part is converted into a circular disc of thickness t and radius 2R. If I1 is moment of inertia of a sphere having radius r about an axis through its centre and I2 is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia I2/I1= .
The position of an object having mass 0.1 kg as a function of time t is given as r= (10t2 i+5t3 j ) m. At t=1 s, which of the following statements are correct? Choose the correct answer from the options given below:
A particle is rotating in a circular path and at any instant its motion can be described as = 5t440- t33. The angular acceleration of the particle after 10 seconds is rad/s2.