Question

A body, under the action of a force $$F = 6\hat i - 8\hat j + 10\hat k,$$    acquires an acceleration of $$1\,m{s^{ - 2}}.$$  The mass of this body must be

A. $$2\sqrt {10} \,kg$$
B. $$10\,kg$$
C. $$20\,kg$$
D. $$10\sqrt 2 \,kg$$  
Answer :   $$10\sqrt 2 \,kg$$
Solution :
$$\eqalign{ & {\text{Here,}}\,F = 6\hat i - 8\hat j + 10\hat k \cr & \left| F \right| = \sqrt {36 + 64 + 100} \cr & = 10\sqrt 2 \,N \cr & a = 1\,m{s^{ - 2}} \cr & \therefore m = \frac{{10\sqrt 2 }}{1}\,\,\left[ {\because F = ma} \right] \cr & = 10\sqrt 2 \,kg \cr} $$

Releted MCQ Question on
Basic Physics >> Laws of Motion

Releted Question 1

A ship of mass $$3 \times {10^7}\,kg$$   initially at rest, is pulled by a force of $$5 \times {10^4}\,N$$   through a distance of $$3m.$$ Assuming that the resistance due to water is negligible, the speed of the ship is

A. $$1.5 m/sec.$$
B. $$60 m/sec.$$
C. $$0.1 m/sec.$$
D. $$5 m/sec.$$
Releted Question 2

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $$\theta $$ should be
Laws of Motion mcq question image

A. $${0^ \circ }$$
B. $${30^ \circ }$$
C. $${45^ \circ }$$
D. $${60^ \circ }$$
Releted Question 3

A string of negligible mass going over a damped pulley of mass $$m$$ supports a block of mass $$M$$ as shown in the figure. The force on the pulley by the clamp is given by
Laws of Motion mcq question image

A. $$\sqrt 2 \,{\text{Mg}}$$
B. $$\sqrt 2 \,{\text{mg}}$$
C. $$\sqrt {{{\left( {M + m} \right)}^2} + {m^2}} g$$
D. $$\sqrt {{{\left( {M + m} \right)}^2} + {M^2}} g$$
Releted Question 4

The string between blocks of mass $$m$$ and $$2m$$ is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut find the magnitudes of accelerations of mass $$2m$$ and $$m$$ (immediately after cutting)
Laws of Motion mcq question image

A. g, g
B. $$g,\frac{g}{2}$$
C. $$\frac{g}{2},g$$
D. $$\frac{g}{2},\frac{g}{2}$$

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