Laws of Motion

A block of mass m is placed on a surface having vertical cross-section given by y=x2/4. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

1. 1/2 m
2. 1/3 m
3. 1/6 m
4. 1/4 m

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure [figure] The tensions T1 and T2 in the string are respectively :

1. 40N, 64N
2. 60N, 80N
3. 80N, 100N
4. 88N, 96N

If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then in order to have constant centripetal force, their velocities will be in the ratio of :

1. 1: 3
2. 2: 3
3. 3:2
4. 3:1

A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if 2=9.8 and g=9.8 m/s2) :

1. 17.8 N
2. 97 N
3. 9.8 N
4. 8.82 N

A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve of radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g=10 m/s2) :

1. 6.0 cm
2. 5.4 cm
3. 4.8 cm
4. 4.2 cm

A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:

1. 6
2. 2
3. 3
4. 5

Given below are two statements : In the light of the above statements, choose the most appropriate answer from the options given below :

1. Statement I is incorrect but Statement II is correct
2. Both Statement I and Statement II are correct
3. Both Statement I and Statement II are incorrect
4. Statement I is correct but Statement II is incorrect