A tangential force acting on the top of a sphere of mass \(m\) kept on a rough horizontal plane as shown in the figure.
If the sphere rolls without slipping, then the acceleration with which the centre of the sphere moves is:
1. \(\frac{10~F}{7~M}\)
2. \(\frac{F}{2~M}\)
3. \(\frac{3~F}{7~M}\)
4. \(\frac{7~F}{2~M}\)
The density of a rod having length \(l\) varies as \(\rho=c+dx,\) where \(x\) is the distance from the left end. The distance from origin to the centre of mass is:
1. \(\frac{3cl+2Dl^2}{3(2c+Dl)}\)
2. \(\frac{3cl+4Dl^2}{3(2c+Dl)}\)
3. \(\frac{2cl+3Dl^2}{3(2c+1)}\)
4. \(\frac{cl+3Dl^2}{3(2c+Dl)}\)
1. 0.1 m
2. 10 cm
3. 1 cm
4. 0.01 cm
A block slides down on an incline of angle 30° with an acceleration \(\frac g4.\) Find the kinetic friction coefficient.
1. \(\frac{1}{2\sqrt2}\)
2. \(0.6\)
3. \(\frac{1}{2\sqrt3}\)
4. \(\frac{1}{\sqrt2}\)
Two long straight wires, each carrying an electric current of 5 A, are kept parallel to each other at a separation of 2.5 cm. Find the magnitude of the magnetic force experiment by 10 cm of a wire.
1. 4.0 × 10-4 N
2. 3.5 × 10-6 N
3. 2.0 × 10-5 N
4. 2.0 × 10-9 N
A wire of resistance 10 Q is bent to form a complete circle. Find its resistance between two diametrically opposite points.
1. \(5~\Omega\)
2. \(2.5~\Omega\)
3. \(1.25~\Omega\)
4. \(\frac{10}{3}~\Omega\)
1. 2.1 x 10-3 \(\Omega\)
2. 1.3 x 10-4 \(\Omega\)
3. 3.2 x 10-4 \(\Omega\)
4. 4.6 x 10-2 \(\Omega\)
1. 50 N
2. 26 N
3. 29 N
4. 45.9 N
3. \( 600 \mathrm{~J}\)
4. \( 900 \mathrm{~J} \)
A uniform ring of mass \(m\) and radius a is placed directly above a uniform sphere of mass m and of equal to radius. The centre of the ring is at a distance \(\sqrt3a\) from the centre of the sphere. The gravitational force (F) exerted by the sphere on the ring is:
1. \(\frac{3G~Mm}{8a^2}\)
2. \(\frac{2G~Mm}{3a^2}\)
3. \(\frac{7G~Mm}{\sqrt2a^2}\)
4. \(\frac{3G~Mm}{a^2}\)